Category:Topology
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This category contains results about Topology.
Definitions specific to this category can be found in Definitions/Topology.
Topology is a geometry of transformations in which the only invariant is continuity.
Some sources suggest that it can indeed be described simply as the study of continuity.
As such, it is closely interwoven with the branch of analysis.
Subcategories
This category has the following 155 subcategories, out of 155 total.
A
- Accumulation Points (8 P)
- Arcs (Topology) (empty)
B
- Baire Property (empty)
- Banach-Tarski Paradox (9 P)
- Borel Sets (1 P)
C
- Category of Open Sets (empty)
- Cells (Topology) (empty)
- Clopen Sets (15 P)
- Cobordisms (empty)
- Cohomology Groups (empty)
- Compactifications (empty)
- Condensation Points (10 P)
- Convergent Sequences (Topology) (empty)
D
- Derived Sets (empty)
- Differential Topology (2 P)
- Dimension Theory (empty)
- Discrete Sets of Subsets (2 P)
E
- Embeddings (Topology) (6 P)
- Everywhere Dense (2 P)
F
- F-Sigma Sets (13 P)
G
- G-Delta Sets (17 P)
- Generic Points of Topological Spaces (empty)
- Geometric Topology (empty)
H
- Hausdorff Paradox (6 P)
I
J
- Jordan Arcs (2 P)
- Jordan Curves (12 P)
K
- Klein Bottle (empty)
L
- Loops (Topology) (5 P)
M
- Morse Theory (empty)
N
- Neighborhood Bases (5 P)
- Nets (Topology) (empty)
- Nowhere Dense (1 P)
O
- Omega-Accumulation Points (8 P)
- Oscillation (5 P)
P
- Paths (Topology) (1 P)
- Perfect Sets (3 P)
- Point-Set Topology (empty)
- Polish Spaces (1 P)
- Proper Mappings (empty)
Q
R
- Regular Closed Sets (4 P)
- Regular Open Sets (4 P)
- Retractions (Topology) (empty)
S
- Schemes (6 P)
- Set Derivatives (13 P)
- Simply Connected Spaces (11 P)
- Sub-Bases (2 P)
- Submanifolds (empty)
- Symplectic Geometry (empty)
T
- Tangent Bundles (2 P)
- Topological Order Theory (34 P)
- Topological Semigroups (empty)
- Topological Sum (2 P)
- Tori (empty)
U
V
- Vector Bundles (empty)
W
- Weakly Hereditary Properties (1 P)
Pages in category "Topology"
The following 112 pages are in this category, out of 112 total.
B
- Baire Characterisation Theorem
- Baire-Osgood Theorem
- Banach-Tarski Paradox
- Basis Condition for Coarser Topology
- Basis Condition for Coarser Topology/Corollary 1
- Basis Condition for Coarser Topology/Corollary 2
- Basis has Subset Basis of Cardinality equal to Weight of Space
- Basis induces Local Basis
- Bottom in Ordered Set of Topology
- Boundary of Polygon is Topological Boundary
- Brouwer's Fixed Point Theorem
C
- Cardinality of Image of Mapping of Intersections is not greater than Weight of Space
- Cesàro Mean
- Characterization of Analytic Basis by Local Bases
- Characterization of Interior of Triangle
- Characterization of Prime Element in Inclusion Ordered Set of Topology
- Characterization of Zero Entropy of Open Cover
- Closed Set in Closed Subspace
- Closed Topologist's Sine Curve is Connected
- Closed Unit Interval is not Countably Infinite Union of Disjoint Closed Sets
- Coarseness Relation on Topologies is Partial Ordering
- Complement of Element is Irreducible implies Element is Meet Irreducible
- Continuous Image of Path-Connected Set is Path-Connected
- Continuous Mapping is Continuous on Induced Topological Spaces
- Continuous Mapping on Finer Domain and Coarser Codomain Topologies is Continuous
- Convex Set is Contractible
- Correspondence between Neighborhood Space and Topological Space
E
- Element is Meet Irreducible iff Complement of Element is Irreducible
- Empty Set is Element of Topology
- Empty Set Satisfies Topology Axioms
- Equidecomposability is Equivalence Relation
- Equidecomposability Unaffected by Union
- Equidecomposable Nested Sets
- Equivalence of Definitions of Continuous Mapping between Topological Spaces at Point
- Equivalence of Definitions of Convergent Sequence in Topology
- Equivalence of Definitions of Everywhere Continuous Mapping between Topological Spaces
- Equivalence of Definitions of Finer Topology
- Equivalence of Definitions of Kuratowski Closure Operator
- Equivalence of Definitions of Topology
- Equivalence of Definitions of Weight of Topological Space
- Every Filter has Limit Point implies Every Ultrafilter Converges
- Existence and Uniqueness of Generated Topology
- Existence of Subfamily of Cardinality not greater than Weight of Space and Unions Equal
- Extendability Theorem for Intersection Numbers/Corollary
F
G
I
J
N
O
P
R
S
- Sequence Lemma
- Sequence on Product Space Converges to Point iff Projections Converge to Projections of Point
- Set of Invertible Continuous Transformations is Open Subset of Continuous Linear Transformations in Supremum Operator Norm Topology
- Shift of Finite Type is Compact
- Subsets of Equidecomposable Subsets are Equidecomposable
T
- Top in Ordered Set of Topology
- Topological Product of Compact Spaces
- Topological Product of Compact Spaces/Finite Product
- Topological Space induced by Neighborhood Space induced by Topological Space
- Topological Space is Open Neighborhood of Subset
- Topologies are not necessarily Comparable by Coarseness
- Topologies on Set form Complete Lattice
- Topology as Magma of Sets
- Topology Defined by Closed Sets
- Topology Defined by Neighborhood System
- Topology forms Complete Lattice
- Topology Generated by Closed Sets
- Topology is Locally Compact iff Ordered Set of Topology is Continuous