Orthocompact space

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.

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

Open $$\to$$ Interior-preserving open

Stronger properties

 * Compact space
 * Paracompact space
 * Metacompact space
 * Alexandroff space
 * Linearly ordered space

Weaker properties

 * Countably orthocompact space