Page "Tychonoff space" Paragraph 37

Given an arbitrary topological space ( X, τ ) there is a universal way of associating a completely regular space with ( X, τ ).

Let ρ be the initial topology on X induced by C < sub > τ </ sub >( X ) or, equivalently, the topology generated by the basis of cozero sets in ( X, τ ).

Then ρ will be the finest completely regular topology on X which is coarser than τ.

This construction is universal in the sense that any continuous function