Borel 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

Symbol-free definition

A Borel map between two topological spaces is a map from one to the other satisfying the following equivalent conditions:

• The inverse image of every open subset is a Borel subset
• The inverse image of every closed subset is a Borel subset
• The inverse image of every Borel subset is a Borel subset

Relation with other properties

Stronger properties

• Borel isomorphism
• Continuous map