pariwise completely regular

Definition

• A bitopological space (X, τ_1, τ_2) is pairwise completely regular if τ_i closed set C and each point there is a real valued function f:X→[0,1] such that f(x)=0 , f(C)={1} , f is τ_i upper semi-continuous and τ_j lower semi-continuous, for .

Property

• Bitopological space (X, τ, μ) is quasi-uniformiziable? if and only if it is pairwise completely regular?.

Reference

• Raghavan, T.G.; Reilly, I.L. ,Uniformization of quasi-uniform spaces. (English) [J] Bull. Aust. Math. Soc. 23, 413-422 (1981).