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