Bitopological space


In mathematics, a bitopological space is a set endowed with two topologies. Typically, if the set is and the topologies are and then the bitopological space is referred to as. The notion was introduced by J. C. Kelly in the study of quasimetrics, i.e. distance functions that are not required to be symmetric.

Continuity

A map from a bitopological space to another bitopological space is called continuous or sometimes pairwise continuous if is continuous both as a map from to and as map from to.

Bitopological variants of topological properties

Corresponding to well-known properties of topological spaces, there are versions for bitopological spaces.