<Ul> <Li> Every subspace of a completely regular or Tychonoff space has the same property . </Li> <Li> A nonempty product space is completely regular (resp . Tychonoff) if and only if each factor space is completely regular (resp . Tychonoff). </Li> </Ul> <Li> Every subspace of a completely regular or Tychonoff space has the same property . </Li> <Li> A nonempty product space is completely regular (resp . Tychonoff) if and only if each factor space is completely regular (resp . Tychonoff). </Li> <P> Like all separation axioms, complete regularity is not preserved by taking final topologies . In particular, quotients of completely regular spaces need not be regular . Quotients of Tychonoff spaces need not even be Hausdorff . There are closed quotients of the Moore plane which provide counterexamples . </P>

Product of completely regular spaces is completely regular