# Category:Topological Order Theory

Jump to navigation
Jump to search

This category contains results about Topological Order Theory.

Definitions specific to this category can be found in Definitions/Topological Order Theory.

**Topological order theory** is the branch of relation theory and topology which studies orderings and topological spaces.

## Pages in category "Topological Order Theory"

The following 34 pages are in this category, out of 34 total.

### C

- Closed Set iff Lower and Closed under Directed Suprema in Scott Topological Ordered Set
- Closed Subset is Upper in Lower Topology
- Closure of Singleton is Lower Closure of Element in Scott Topological Lattice
- Complement of Lower Closure is Prime Element in Inclusion Ordered Set of Scott Sigma
- Complement of Lower Closure of Element is Open in Scott Topological Ordered Set
- Complement of Upper Closure of Element is Open in Lower Topology
- Continuous iff Directed Suprema Preserving
- Continuous iff Mapping at Element is Supremum
- Continuous iff Mapping at Element is Supremum of Compact Elements
- Continuous iff Mapping at Limit Inferior Precedes Limit Inferior of Composition of Mapping and Sequence
- Continuous iff Way Below iff There Exists Element that Way Below and Way Below
- Continuous implies Increasing in Scott Topological Lattices

### I

### L

### M

- Mapping is Continuous implies Mapping Preserves Filtered Infima in Lower Topological Lattice
- Mapping Preserves Directed Suprema implies Mapping is Continuous
- Mapping Preserves Infima implies Mapping is Continuous in Lower Topological Lattice
- Mapping Preserves Non-Empty Infima implies Mapping is Continuous in Lower Topological Lattice