In mathematics, a bitopological space is a set endowed with two topologies.
Typically, if the set is
and the topologies are
σ
τ
then the bitopological space is referred to as
, σ , τ )
The notion was introduced by J. C. Kelly in the study of quasimetrics, i.e. distance functions that are not required to be symmetric.
A map
from a bitopological space
τ
to another bitopological space
is called continuous or sometimes pairwise continuous if
is continuous both as a map from
and as map from
Corresponding to well-known properties of topological spaces, there are versions for bitopological spaces.