Submaximal 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

Definition

Symbol-free definition

A topological space is termed submaximal if every subset of it is locally closed, viz, an intersection of an open subset and a closed subset.

In particular, this means that every dense subset is open.

Relation with other properties

Stronger properties

• Door space

Weaker properties

• Weakly submaximal space