N-topological space

In mathematics, an N-topological space is a set equipped with N arbitrary topologies.

If τ1, τ2, ..., τN are N topologies defined on a nonempty set X, then the N-topological space is denoted by (X,τ1,τ2,...,τN).

For N = 1, the structure is simply a topological space.

For N = 2, the structure becomes a bitopological space introduced by J. C.

If τ1, τ2, ..., τm be m such topologies (chain topologies) defined on X, then the structure (X, τ1, τ2, ..., τm) is an m-topological space.