Also called a -space, a Tychonoff space is a completely regular space (with the additional condition that it be for those authors who do not assume this in the definition of completely regular.) In any case, Tychonoff spaces can be characterized as the topological spaces which are homeomorphic to a subspace of some cube (equivalently, which are subspaces of some compact T2-space, or some T4-space.)

# Tychonoff Space

*This entry contributed by Margherita
Barile*

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## References

Cullen, H. F.*Introduction to General Topology.*Boston, MA: Heath, 1968.Joshi, K. D.

*Introduction to General Topology.*New Delhi, India: Wiley, 1983.Kelley, J. L.

*General Topology.*New York: Van Nostrand, 1955.Willard, S.

*General Topology.*Reading, MA: Addison-Wesley, 1970.

## Referenced on Wolfram|Alpha

Tychonoff Space## Cite this as:

Barile, Margherita. "Tychonoff Space." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/TychonoffSpace.html