# Category:Way Below Relation

This category contains results about the way below relation.

## Pages in category "Way Below Relation"

The following 65 pages are in this category, out of 65 total.

### A

### B

### C

- Characterization of Pseudoprime Element when Way Below Relation is Multiplicative
- Compact Closure is Directed
- Compact Closure is Increasing
- Compact Closure is Intersection of Lower Closure and Compact Subset
- Compact Closure is Set of Finite Subsets in Lattice of Power Set
- Compact Closure is Subset of Way Below Closure
- Compact Closure of Element is Principal Ideal on Compact Subset iff Element is Compact
- Compact Element iff Existence of Finite Subset that Element equals Intersection and Includes Subset
- Compact Element iff Principal Ideal
- Compact Subset is Join Subsemilattice
- Continuous iff Mapping at Element is Supremum
- Continuous iff Mapping at Element is Supremum of Compact Elements
- Continuous iff Way Below Closure is Ideal and Element Precedes Supremum
- Continuous iff Way Below iff There Exists Element that Way Below and Way Below

### I

- If Compact Between then Way Below
- If Every Element Pseudoprime is Prime then Way Below Relation is Multiplicative
- Image of Compact Subset under Directed Suprema Preserving Closure Operator
- Image of Compact Subset under Directed Suprema Preserving Closure Operator is Subset of Compact Subset
- Infimum of Open Set is Way Below Element in Complete Scott Topological Lattice
- Intersection of Applications of Down Mappings at Element equals Way Below Closure of Element
- Intersection of Ideals with Suprema Succeed Element equals Way Below Closure of Element

### M

- Mapping Assigning to Element Its Compact Closure Preserves Infima and Directed Suprema
- Mapping at Element is Supremum implies Way Below iff There Exists Element that Way Below and Way Below
- Mapping at Element is Supremum of Compact Elements implies Mapping at Element is Supremum that Way Below
- Mapping at Element is Supremum of Compact Elements implies Mapping is Increasing

### P

### W

- Way Above Closure is Upper
- Way Above Closures that Way Below Form Local Basis
- Way Below Closure is Directed in Bounded Below Join Semilattice
- Way Below Closure is Ideal in Bounded Below Join Semilattice
- Way Below Closure is Lower Set
- Way Below Compact is Topological Compact
- Way Below has Interpolation Property
- Way Below has Strong Interpolation Property
- Way Below if Between is Compact Set in Ordered Set of Topology
- Way Below iff Preceding Finite Supremum
- Way Below iff Second Operand Preceding Supremum of Directed Set There Exists Element of Directed Set First Operand Way Below Element
- Way Below iff Second Operand Preceding Supremum of Ideal implies First Operand is Element of Ideal
- Way Below iff Second Operand Preceding Supremum of Prime Ideal implies First Operand is Element of Ideal
- Way Below implies Preceding
- Way Below in Complete Lattice
- Way Below in Lattice of Power Set
- Way Below in Meet-Continuous Lattice
- Way Below in Ordered Set of Topology
- Way Below is Approximating Relation
- Way Below is Congruent for Join
- Way Below Relation is Antisymmetric
- Way Below Relation is Auxiliary Relation
- Way Below Relation is Multiplicative implies Pseudoprime Element is Prime
- Way Below Relation is Transitive