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

A topological space is termed submaximal if it satisfies the following equivalent conditions:

1. Every subset of it is locally closed, i.e., an intersection of an open subset and a closed subset.
2. Every dense subset is open.
3. Every preopen subset is open.

Relation with other properties

Stronger properties

• Door space

Weaker properties

• Weakly submaximal space