locally compact with respect to τ

Definition

• For a bitopological space (X,τ_1,τ_2), the topology τ_i is called locally compact with respect to the topology τ_j if each each point of X has τ_j neighbourhood which is τ_i compact.

Definitnion 2

• For a bitopological space (X, τ_1, τ_2) , the topology τ_i is locally compact with respect to τ_j if each point of X has a τ_i open neighborhood whose τ_j-closure is pairwise compact (Definition 1).

Reference

Definition

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

Definition 2

Rina Verma, On Pairwise H-Singular Maps., Int.J.Contemp.Math.Schieces, Vol. 6, 2011, no. 2, 51-58