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

History

Origin

The concept of orthocompactness was introduced by Sion and Willmott, as spaces having property Q. The name orthocompact was given by Arens.

Definition

A topological space is said to be orthocompact if it satisfies the following condition: every open cover has an interior-preserving open refinement.

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
• Alexandroff space
• Linearly ordered space

Weaker properties

• Countably orthocompact space

References

• Hausdorff measures on abstract spaces by M. Sion and R. C. Willmott, Transactions, American Mathematical Society, 123 (1966), 275-309