Complete regularity is product-closed

This article gives the statement, and possibly proof, of a topological space property (i.e., completely regular space) not satisfying a topological space metaproperty (i.e., product-closed property of topological spaces).
View all topological space metaproperty dissatisfactions | View all topological space metaproperty satisfactions|Get help on looking up metaproperty (dis)satisfactions for topological space properties
Get more facts about completely regular space|Get more facts about product-closed property of topological spaces|

Statement

Suppose $X_{i},i\in I$ , are topological spaces that are all completely regular spaces. Then, the product space $\prod _{i\in I}X_{i}$ , endowed with the product topology, is also a completely regular space.

Related facts

Similar facts