J Austral Math Soc Ser A 44 pp271--274, 1988.

Characterizations of Quasi-Metrizable Bitopological Spaces

T. G. Raghavan and I. L. Reilly

Abstract

In this paper we prove that a pairwise Hausdorff bitopological space (X, J₁, J₂) is quasi-metrizable if and only if for each point x Î X and for i, j = 1, 2, i ¹ j, one can assign J_i nbd bases {S(n, i; x) | n = 1, 2, ...} such that (i) y Ï S(n - 1,i; x) implies S(n, i; x) ÇS(n, j; y) = f, (ii) y Î S(n,i; x) implies S(n,i; y) Ì S(n - 1,i; x). We derive two further results from this.

1980 AMS Subject Classification: 54E55

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Authors

T. G. Raghavan

I. L. Reilly

Department of Mathematics, University of Auckland, Private Bag, Auckland, New Zealand.