Orthocompact space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

This is a variation of compactness. View other variations of compactness

Definition

A topological space is said to be orthocompact if it satisfies the following condition: every open cover has an open refinement with the property that the intersection of all the members containing a particular point, is open.

Formalisms

Refinement formal expression

In the refinement formalism, the property of being orthocompact has the following refinement formal expression:

Open $\to$ Interior-preserving open

Relation with other properties

Stronger properties

• Compact space
• Paracompact space
• Metacompact space

Weaker properties

• Countably orthocompact space