# compact

## Primary tabs

Defines:
compact set, compact subset
Type of Math Object:
Definition
Major Section:
Reference
Groups audience:

## Mathematics Subject Classification

### Historical note and terminology

Maybe it would be a good idea to mention that
in some european (especially russian) literature
what is known as compact used to be referred
to as "bicompact", and "compact" referred to
what is now known as countably compact.

Also, I've seen references to "bicompact" meaning
compact and Hausdorff.

My sources are
L. S. Pontriagin. _Continuous Groups_. National Publishing House for Technico-Theoretical Literature, 2nd edition, Moscow: 1954.

http://cm.bell-labs.com/who/will/CAARMS5/williams.pdf

Since some authors require compact spaces to be Hausdorff and others don't, it is apropriate to mention this fact in the article. But I wonder if PlanetMath should adopt one convention, so that everybody's automatic links to the compact article will give the proper definition. Otherwise, everybody has to state explicitly in every article what they mean when they say compact.

I think it's clear by now that the non-Hausdorff definition of compact has won out in modern literature. Therefore planetmath should adopt the convention that compact spaces are not necessarily Hausdorff. Since people seem to be doing this anyway, I don't think anything else needs to be done.