nLab
bitopological space

Bitopological spaces

Definitions

Recall that a topological space is a set equipped with a topological structure. Well, a bitopological space is simply a set equipped with two topological strucutres. Unlike with bialgebras, no compatibility condition is required between these structures.

A bicontinous map is a function between bitopological spaces that is continuous with respect to each topological structures.

Bitopological spaces and bicontinuous maps form a category BiTopBi Top.

Remarks

It is interesting and perhaps surprising that many advanced topological notions can be described using bitopological spaces, even when you would not naïvely think that there are two topologies around. (At least, that's my vague memory of what they were good for. I think that this was in some article by Isbell.)

References

Revised on July 9, 2010 00:53:58 by Toby Bartels (173.60.119.197)