Orthocompact space

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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



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


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

Relation with other properties

Stronger properties

Weaker properties


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