Complete regularity is product-closed

This article gives the statement, and possibly proof, of a topological space property (i.e., completely regular space) satisfying a topological space metaproperty (i.e., product-closed property of topological spaces)
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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

• Regularity is product-closed
• Hausdorffness is product-closed