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.
For N = 1, the structure is simply a topological space.
For N = 2, the structure becomes a bitopological space introduced by J. C. Kelly.

Example

Let X = be any finite set. Suppose Ar = . Then the collection τ1 = will be a topology on X. If τ1, τ2,..., τm be m such topologies defined on X, then the structure is an m-topological space.