# Supercompact space

From Topospaces

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

## Contents

## 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

### 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.