Open map

This article defines a property that can be evaluated for a map between topological spaces. Note that the map is not assumed to be continuous

Definition

A continuous map of topological spaces is termed an open map if the image of any open subset of the domain space is an open subset of the range space.

Relation with other properties

Stronger properties

• Homeomorphism
• Covering map
• Local homeomorphism

Weaker properties

• Quotient map
• Inductively open map