Tychonoff space

Summary

A Tychonoff space is a T1 space with many continuous real functions. Every point can be separated by such a function from every closed set that does not contain it. Such spaces are exactly the subspaces of products of copies of $[0, 1]$, up to homeomorphism. They are also exactly the spaces that embed in some compact Hausdorff space. Metric spaces and compact Hausdorff spaces are Tychonoff.