Supercompact 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 termed supercompact if it has a subbasis such that any open cover of the topological space whose elements come from the subbasis, has a subcover comprising at most two members.

Relation with other properties

Stronger properties

• Compact metrizable space
• Compact linearly orderable space

Weaker properties

• Compact space: For full proof, refer: Alexander subbase theorem

Metaproperties

Products

This property of topological spaces is closed under taking arbitrary products
View all properties of topological spaces closed under products

An arbitrary product of supercompact spaces is supercompact, in the product topology.