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Characterizations of Quasi-Metrizable Bitopological Spaces

Published online by Cambridge University Press:  09 April 2009

T. G. Raghavan
Affiliation:
Department of MathematicsUniversity of AucklandPrivate Bag, Auckland, New Zealand
I. L. Reilly
Affiliation:
Department of MathematicsUniversity of AucklandPrivate Bag, Auckland, New Zealand
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Abstract

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In this paper we prove that a pairwise Hausdorff bitopological space is quasi-metrizable if and only if for each point xX and for i, j = 1,2, ij, one can assign nbd bases { S(n, i; x) | n = 1, 2,… } such that (i) yS (n − 1, i; x) imples S(n, i; x) ∩ S (n, j; y) = φ, (ii) yS (n, i; x) implies S (n, i; y) ⊂ S(n − 1, i; x). We derive two further results from this.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1988

References

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