Pages that link to "Mathematician:Gerhard Gierz"
Jump to navigation
Jump to search
The following pages link to Mathematician:Gerhard Gierz:
Displayed 3 items.
- Mathematician:Mathematicians/Minor Mathematicians (transclusion) (← links)
- Mathematician:G. Gierz (redirect page) (← links)
- Directed iff Finite Subsets have Upper Bounds (← links)
- Filtered iff Finite Subsets have Lower Bounds (← links)
- Singleton is Directed and Filtered Subset (← links)
- Directed iff Lower Closure Directed (← links)
- Filtered iff Upper Closure Filtered (← links)
- Directed in Join Semilattice (← links)
- Filtered in Meet Semilattice (← links)
- Directed in Join Semilattice with Finite Suprema (← links)
- Filtered in Meet Semilattice with Finite Infima (← links)
- Existence of Non-Empty Finite Suprema in Join Semilattice (← links)
- Existence of Non-Empty Finite Infima in Meet Semilattice (← links)
- Mapping Preserves Finite and Filtered Infima (← links)
- Mapping Preserves Finite and Directed Suprema (← links)
- Infima Preserving Mapping on Filters is Increasing (← links)
- Upper Closure of Element is Filter (← links)
- Infimum of Upper Closure of Element (← links)
- Lower Closure of Element is Ideal (← links)
- Supremum of Lower Closure of Element (← links)
- Upper Closure is Decreasing (← links)
- Lower Closure is Increasing (← links)
- Suprema Preserving Mapping on Ideals is Increasing (← links)
- Infima Preserving Mapping on Filters Preserves Filtered Infima (← links)
- Suprema Preserving Mapping on Ideals Preserves Directed Suprema (← links)
- Up-Complete Lower Bounded Join Semilattice is Complete (← links)
- Lattice is Complete iff it Admits All Suprema (← links)
- Galois Connection is Expressed by Minimum (← links)
- Galois Connection is Expressed by Maximum (← links)
- Upper Adjoint Preserves All Infima (← links)
- Lower Adjoint Preserves All Suprema (← links)
- All Infima Preserving Mapping is Upper Adjoint of Galois Connection (← links)
- All Suprema Preserving Mapping is Lower Adjoint of Galois Connection (← links)
- Galois Connection Implies Order on Mappings (← links)
- Ordering on Mappings Implies Galois Connection (← links)
- Shift Mapping is Lower Adjoint iff Appropriate Maxima Exist (← links)
- Brouwerian Lattice iff Shift Mapping is Lower Adjoint (← links)
- Brouwerian Lattice is Distributive (← links)
- Brouwerian Lattice is Upper Bounded (← links)
- Relative Pseudocomplement and Shift Mapping form Galois Connection in Brouwerian Lattice (← links)
- Inequality with Meet Operation is Equivalent to Inequality with Relative Pseudocomplement in Brouwerian Lattice (← links)
- Top equals to Relative Pseudocomplement in Brouwerian Lattice (← links)
- Up-Complete Product (← links)
- Up-Complete Product/Lemma 1 (← links)
- Up-Complete Product/Lemma 2 (← links)
- Meet-Continuous iff Ideal Supremum is Meet Preserving (← links)
- Lower Closure of Meet of Lower Closures (← links)
- Meet Preserves Directed Suprema (← links)
- Supremum of Meet Image of Directed Set (← links)
- Meet Preserves Directed Suprema/Lemma 2 (← links)
- Supremum by Suprema of Directed Set in Simple Order Product (← links)
- Meet is Directed Suprema Preserving implies Meet of Suprema equals Supremum of Meet of Directed Subsets (← links)
- Meet of Suprema equals Supremum of Meet of Ideals implies Ideal Supremum is Meet Preserving (← links)
- Supremum of Simple Order Product (← links)
- Meet-Continuous iff Meet of Suprema equals Supremum of Meet of Ideals (← links)
- Meet-Continuous iff Meet of Suprema equals Supremum of Meet of Directed Subsets (← links)
- Brouwerian Lattice iff Meet-Continuous and Distributive (← links)
- Shift Mapping is Lower Adjoint iff Meet is Distributive with Supremum (← links)
- Meet-Continuous iff Meet Preserves Directed Suprema (← links)
- Meet-Continuous implies Shift Mapping Preserves Directed Suprema (← links)
- Meet-Continuous and Distributive implies Shift Mapping Preserves Finite Suprema (← links)
- Way Below implies Preceding (← links)
- Preceding and Way Below implies Way Below (← links)
- Join is Way Below if Operands are Way Below (← links)
- Way Below Relation is Transitive (← links)
- Way Below Relation is Antisymmetric (← links)
- Way Below iff Preceding Finite Supremum (← links)
- Way Below iff Second Operand Preceding Supremum of Ideal implies First Operand is Element of Ideal (← links)
- Lower Closure of Directed Subset is Ideal (← links)
- Way Below in Meet-Continuous Lattice (← links)
- Set of Finite Suprema is Directed (← links)
- Axiom of Approximation in Up-Complete Semilattice (← links)
- Operand is Upper Bound of Way Below Closure (← links)
- Way Below in Ordered Set of Topology (← links)
- Way Below in Complete Lattice (← links)
- Way Below Compact is Topological Compact (← links)
- Topology is Locally Compact iff Ordered Set of Topology is Continuous (← links)
- Way Below Closure is Directed in Bounded Below Join Semilattice (← links)
- Bottom is Way Below Any Element (← links)
- Way Below if Between is Compact Set in Ordered Set of Topology (← links)
- Auxiliary Relation is Congruent (← links)
- Auxiliary Relation is Transitive (← links)
- Preceding is Auxiliary Relation (← links)
- Preceding is Top in Ordered Set of Auxiliary Relations (← links)
- Bottom Relation is Auxiliary Relation (← links)
- Bottom Relation is Bottom in Ordered Set of Auxiliary Relations (← links)
- Intersection of Auxiliary Relations is Auxiliary Relation (← links)
- Ordered Set of Auxiliary Relations is Complete Lattice (← links)
- Way Below Relation is Auxiliary Relation (← links)
- Relation Segment of Auxiliary Relation is Ideal (← links)
- Correctness of Definition of Increasing Mappings Satisfying Inclusion in Lower Closure (← links)
- Segment of Auxiliary Relation is Subset of Lower Closure (← links)
- Preceding implies Inclusion of Segments of Auxiliary Relation (← links)
- Segment of Auxiliary Relation Mapping is Increasing (← links)
- Segment of Auxiliary Relation Mapping is Element of Increasing Mappings Satisfying Inclusion in Lower Closure (← links)
- Element of Increasing Mappings Satisfying Inclusion in Lower Closure is Generated by Auxiliary Relation (← links)
- Increasing Mappings Satisfying Inclusion in Lower Closure is Isomorphic to Auxiliary Relations (← links)
- Intersection of Ideals with Suprema Succeed Element equals Way Below Closure of Element (← links)
- Way Below Closure is Ideal in Bounded Below Join Semilattice (← links)
- Meet-Continuous iff if Element Precedes Supremum of Directed Subset then Element equals Supremum of Meet of Element by Directed Subset (← links)
- Continuous Lattice is Meet-Continuous (← links)
- Down Mapping is Generated by Approximating Relation (← links)
- Preceding is Approximating Relation (← links)
- Way Below is Approximating Relation (← links)
- Intersection of Relation Segments of Approximating Relations equals Way Below Closure (← links)
- Intersection of Applications of Down Mappings at Element equals Way Below Closure of Element (← links)
- Intersection of Lower Closure of Element with Ideal equals Meet of Element and Ideal (← links)
- Continuous iff Meet-Continuous and There Exists Smallest Auxiliary Approximating Relation (← links)
- Continuous Lattice iff Auxiliary Approximating Relation is Superset of Way Below Relation (← links)
- Not Preceding implies Approximating Relation and not Preceding (← links)
- Auxiliary Approximating Relation has Quasi Interpolation Property (← links)
- Auxiliary Approximating Relation has Interpolation Property (← links)
- Way Below has Strong Interpolation Property (← links)
- Way Below has Interpolation Property (← links)
- Way Below iff Second Operand Preceding Supremum of Directed Set There Exists Element of Directed Set First Operand Way Below Element (← links)
- Continuous iff Way Below Closure is Ideal and Element Precedes Supremum (← links)
- Way Below Closure is Lower Section (← links)
- Continuous iff For Every Element There Exists Ideal Element Precedes Supremum (← links)
- Supremum of Ideals is Upper Adjoint (← links)
- Supremum of Ideals is Increasing (← links)
- Supremum of Ideals is Upper Adjoint implies Lattice is Continuous (← links)
- Continuous Lattice and Way Below implies Preceding implies Preceding (← links)
- Top is Meet Irreducible (← links)
- Meet Irreducible iff Finite Infimum equals Element (← links)
- Upper Closure of Element without Element is Filter implies Element is Meet Irreducible (← links)
- Maximal Element of Complement of Filter is Meet Irreducible (← links)
- Not Preceding implies There Exists Meet Irreducible Element Not Preceding (← links)
- Way Below implies There Exists Way Below Open Filter Subset of Way Above Closure (← links)
- Union of Upper Sections is Upper (← links)
- Union of Filtered Sets is Filtered (← links)
- Way Above Closure is Subset of Upper Closure of Element (← links)
- Upper Way Below Open Subset Complement is Non Empty implies There Exists Maximal Element of Complement (← links)
- Order Generating iff Every Element is Infimum (← links)
- Order Generating iff Every Superset Closed on Infima is Whole Space (← links)
- Order Generating iff Not Preceding implies There Exists Element Preceding and Not Preceding (← links)
- Set of Meet Irreducible Elements Excluded Top is Order Generating (← links)
- Superset of Order Generating is Order Generating (← links)
- Top is Prime Element (← links)
- Characterization of Prime Element in Meet Semilattice (← links)
- Prime Element is Meet Irreducible (← links)
- Prime Element iff Meet Irreducible in Distributive Lattice (← links)
- Prime Element iff Complement of Lower Closure is Filter (← links)
- Prime Element iff Element Greater is Top (← links)
- Prime Element iff There Exists Way Below Open Filter which Complement has Maximum (← links)
- Characterization of Prime Ideal (← links)
- Prime Ideal is Prime Element (← links)
- Characterization of Prime Ideal by Finite Infima (← links)
- Characterization of Prime Filter by Finite Suprema (← links)
- Prime Ideal is Prime Filter in Dual Lattice (← links)
- Prime Filter is Prime Ideal in Dual Lattice (← links)
- Filter is Prime iff For Every Element Element either Negation Belongs to Filter in Boolean Lattice (← links)
- Proper and Prime iff Ultrafilter in Boolean Lattice (← links)
- Finite Subset Bounds Element of Finite Infima Set and Upper Closure (← links)
- If Ideal and Filter are Disjoint then There Exists Prime Ideal Including Ideal and Disjoint from Filter (← links)
- Finite Subset Bounds Element of Finite Suprema Set and Lower Closure (← links)
- If Element Does Not Belong to Ideal then There Exists Prime Ideal Including Ideal and Excluding Element (← links)
- If Ideal and Filter are Disjoint then There Exists Prime Filter Including Filter and Disjoint from Ideal (← links)
- Proper Filter is Included in Ultrafilter in Boolean Lattice (← links)
- Way Below iff Second Operand Preceding Supremum of Prime Ideal implies First Operand is Element of Ideal (← links)
- Lower Closure is Prime Ideal for Prime Element (← links)
- Prime is Pseudoprime (Order Theory) (← links)
- Characterization of Pseudoprime Element by Finite Infima (← links)
- Multiplicative Auxiliary Relation iff Images are Filtered (← links)
- Multiplicative Auxiliary Relation iff Congruent (← links)
- Characterization of Pseudoprime Element when Way Below Relation is Multiplicative (← links)
- Way Below Relation is Multiplicative implies Pseudoprime Element is Prime (← links)
- If Every Element Pseudoprime is Prime then Way Below Relation is Multiplicative (← links)
- Upper Closure of Element is Way Below Open Filter iff Element is Compact (← links)
- If Compact Between then Way Below (← links)
- Way Below is Congruent for Join (← links)
- Compact Subset is Join Subsemilattice (← links)
- Bottom in Compact Subset (← links)
- Compact Closure is Intersection of Lower Closure and Compact Subset (← links)
- Compact Closure is Subset of Way Below Closure (← links)
- Algebraic iff Continuous and For Every Way Below Exists Compact Between (← links)
- Non-Empty Way Below Closure is Directed in Join Semilattice (← links)
- Arithmetic iff Way Below Relation is Multiplicative in Algebraic Lattice (← links)
- Arithmetic iff Compact Subset form Lattice in Algebraic Lattice (← links)
- Pseudoprime Element is Prime in Arithmetic Lattice (← links)
- Every Pseudoprime Element is Prime implies Lattice is Arithmetic (← links)
- Element is Finite iff Element is Compact in Lattice of Power Set (← links)
- Way Below in Lattice of Power Set (← links)
- Compact Closure is Set of Finite Subsets in Lattice of Power Set (← links)
- Lattice of Power Set is Algebraic (← links)
- Ordering on Closure Operators iff Images are Including (← links)
- Ordered Set of Closure Systems is Ordered Set (← links)
- Image of Closure Operator Inherits Infima (← links)
- Closure Operator does not Change Infimum of Subset of Image (← links)
- Operator Generated by Closure System is Closure Operator (← links)
- Image of Operator Generated by Closure System is Set of Closure System (← links)
- Operator Generated by Image of Closure Operator is Closure Operator (← links)
- Ordered Set of Closure Operators and Dual Ordered Set of Closure Systems are Isomorphic (← links)
- Operator Generated by Closure System Preserves Directed Suprema iff Closure System Inherits Directed Suprema (← links)
- Closure Operator Preserves Directed Suprema iff Image of Closure Operator Inherits Directed Suprema (← links)
- Closed Set iff Lower and Closed under Directed Suprema in Scott Topological Ordered Set (← links)
- Closure of Singleton is Lower Closure of Element in Scott Topological Lattice (← links)
- Scott Topological Lattice is T0 Space (← links)
- Lower Closure of Element is Topologically Closed in Scott Topological Ordered Set (← links)
- Complement of Lower Closure of Element is Open in Scott Topological Ordered Set (← links)
- Open iff Upper and with Property (S) in Scott Topological Lattice (← links)
- Relational Structure with Topology of Subsets with Property (S) is Topological Space (← links)
- Coarser Between Generator Set and Filter is Generator Set of Filter (← links)
- Finite Infima Set of Coarser Subset is Coarser than Finite Infima Set (← links)
- Upper Closure of Coarser Subset is Subset of Upper Closure (← links)
- Set Coarser than Upper Section is Subset (← links)
- Image of Mapping of Infima is Generator Set of Filter (← links)
- Complement of Element is Irreducible implies Element is Meet Irreducible (← links)
- Element is Meet Irreducible iff Complement of Element is Irreducible (← links)
- Element of Ordered Set of Topology is Dense iff is Everywhere Dense (← links)
- Compact Element iff Principal Ideal (← links)
- Ideals are Continuous Lattice Subframe of Power Set (← links)
- Compact Element iff Existence of Finite Subset that Element equals Intersection and Includes Subset (← links)
- Image of Compact Subset under Directed Suprema Preserving Closure Operator (← links)
- Mapping Assigning to Element Its Lower Closure is Isomorphism (← links)
- Ideals form Arithmetic Lattice (← links)
- Ideals form Algebraic Lattice (← links)
- Continuous Lattice Subframe of Algebraic Lattice is Algebraic Lattice (← links)
- Image of Directed Suprema Preserving Closure Operator is Algebraic Lattice (← links)
- Compact Subset is Bounded Below Join Semilattice (← links)
- Compact Closure of Element is Principal Ideal on Compact Subset iff Element is Compact (← links)
- Image of Compact Subset under Directed Suprema Preserving Closure Operator is Subset of Compact Subset (← links)
- Mapping Assigning to Element Its Compact Closure Preserves Infima and Directed Suprema (← links)
- Mapping Assigning to Element Its Compact Closure is Order Isomorphism (← links)
- Complement of Irreducible Topological Subset is Prime Element (← links)
- Infimum of Open Set is Way Below Element in Complete Scott Topological Lattice (← links)
- Complement of Lower Closure is Prime Element in Inclusion Ordered Set of Scott Sigma (← links)
- Element equals to Supremum of Infima of Open Sets that Element Belongs implies Topological Lattice is Continuous (← links)
- Set of Upper Closures of Compact Elements is Basis implies Complete Scott Topological Lattice is Algebraic (← links)
- Lattice of Power Set is Arithmetic (← links)
- Completely Irreducible Element iff Exists Element that Strictly Succeeds First Element (← links)
- Completely Irreducible and Subset Admits Infimum Equals Element implies Element Belongs to Subset (← links)
- Order Generating Subset Includes Completely Irreducible Elements (← links)
- Maximal implies Completely Irreducible (← links)
- Set of All Completely Irreducible Elements is Smallest Order Generating (← links)
- Completely Irreducible Element equals Infimum of Subset implies Element Belongs to Subset (← links)
- Continuous implies Increasing in Scott Topological Lattices (← links)
- Mapping at Limit Inferior Precedes Limit Inferior of Composition Mapping and Sequence implies Supremum of Image is Mapping at Supremum of Directed Subset (← links)
- Mapping at Limit Inferior Precedes Limit Inferior of Composition Mapping and Sequence implies Mapping Preserves Directed Suprema (← links)
- Mapping Preserves Directed Suprema implies Mapping is Continuous (← links)
- Continuous iff Mapping at Limit Inferior Precedes Limit Inferior of Composition of Mapping and Sequence (← links)
- Mapping is Increasing implies Mapping at Infimum for Sequence Precedes Infimum for Composition of Mapping and Sequence (← links)
- Continuous iff Directed Suprema Preserving (← links)
- Continuous iff Way Below iff There Exists Element that Way Below and Way Below (← links)
- Open implies There Exists Way Below Element (← links)
- Interior is Union of Way Above Closures (← links)
- Way Above Closures Form Basis (← links)
- Way Above Closure is Open (← links)
- Way Above Closures that Way Below Form Local Basis (← links)
- Mapping at Element is Supremum of Compact Elements implies Mapping is Increasing (← links)
- Mapping at Element is Supremum of Compact Elements implies Mapping at Element is Supremum that Way Below (← links)
- Continuous iff Mapping at Element is Supremum (← links)
- Continuous iff Mapping at Element is Supremum of Compact Elements (← links)
- Relational Structure admits Lower Topology (← links)
- Lower Topology is Unique (← links)
- Simple Order Product of Pair of Ordered Sets is Ordered Set (← links)
- All Infima Preserving Mapping is Upper Adjoint of Galois Connection/Lemma 2 (← links)
- All Infima Preserving Mapping is Upper Adjoint of Galois Connection/Lemma 1 (← links)
- User:GFauxPas/Sandbox (← links)
- Axiom:Axiom of Approximation (← links)
- Axiom:Axiom of K-Approximation (← links)
- Definition:Directed Subset (← links)
- Definition:Filtered Subset (← links)
- Definition:Mapping Preserves Supremum (← links)
- Definition:Mapping Preserves Supremum/Subset (← links)
- Definition:Mapping Preserves Supremum/All (← links)
- Definition:Mapping Preserves Supremum/Join (← links)
- Definition:Mapping Preserves Supremum/Finite (← links)
- Definition:Mapping Preserves Supremum/Directed (← links)
- Definition:Mapping Preserves Infimum/Subset (← links)
- Definition:Mapping Preserves Infimum/All (← links)
- Definition:Mapping Preserves Infimum/Meet (← links)
- Definition:Mapping Preserves Infimum/Finite (← links)
- Definition:Mapping Preserves Infimum (← links)
- Definition:Mapping Preserves Infimum/Filtered (← links)
- Definition:Filter in Ordered Set (← links)
- Definition:Ideal in Ordered Set (← links)
- Definition:Up-Complete (← links)
- Definition:Galois Connection (← links)
- Definition:Ordering on Mappings (← links)
- Definition:Meet-Continuous Lattice (← links)
- Definition:Element is Way Below (← links)
- Definition:Way Below Closure (← links)
- Definition:Continuous Ordered Set (← links)
- Definition:Auxiliary Relation (← links)
- Definition:Increasing Mappings Satisfying Inclusion in Lower Closure (← links)
- Definition:Approximating Relation (← links)
- Definition:Meet Irreducible Element (← links)
- Definition:Way Below Open (← links)
- Definition:Way Above Closure (← links)
- Definition:Order Generating Subset (← links)
- Definition:Prime Element (Order Theory) (← links)
- Definition:Prime Filter (Order Theory) (← links)
- Definition:Pseudoprime (Order Theory) (← links)
- Definition:Compact Subset of Lattice (← links)
- Definition:Compact Closure (← links)
- Definition:Algebraic Ordered Set (← links)
- Definition:Compact Element (← links)
- Definition:Ordered Set of Closure Operators (← links)
- Definition:System (Order Theory) (← links)
- Definition:Closure System (← links)
- Definition:Ordered Set of Closure Systems (← links)
- Definition:Operator Generated by Ordered Subset (← links)
- Definition:Ordered Set of Subalgebras (← links)
- Definition:Inaccessible by Directed Suprema (← links)
- Definition:Closed under Directed Suprema (← links)
- Definition:Property (S) (← links)
- Definition:Scott Topology (← links)
- Definition:Topological Lattice (← links)
- Definition:Limit Inferior of Net (← links)
- Definition:Generator Set of Filter (← links)
- Definition:Continuous Lattice Subframe (← links)
- Definition:Scott Sigma (← links)
- Definition:Jointly Scott Continuous (← links)
- Definition:Completely Irreducible (← links)
- Definition:Injective Space (← links)
- Definition:Lower Topology (← links)
- Definition:Simple Order Product (← links)
- Definition:Galois Connection/Upper Adjoint (← links)
- Definition:Galois Connection/Lower Adjoint (← links)
- Mathematician:Mathematicians/Minor Mathematicians (← links)
- Mathematician:Dana Stewart Scott (← links)
- Mathematician:Karl Heinrich Hofmann (← links)
- Mathematician:Klaus Keimel (← links)
- Mathematician:Jimmie D. Lawson (← links)
- Mathematician:Michael W. Mislove (← links)
- Mathematician:Mathematicians/Minor Mathematicians/K (← links)
- Mathematician:Mathematicians/Minor Mathematicians/L (← links)
- Mathematician:Mathematicians/Minor Mathematicians/M (← links)
- Book:Books (← links)
- Book:Books/Abstract Algebra (← links)
- Book:G. Gierz/A Compendium of Continuous Lattices (← links)
- Mathematician:Mathematicians/Minor Mathematicians/G (transclusion) (← links)