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Characterizations of Quasi-Metrizable Bitopological Spaces

Part of: Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

T. G. Raghavan  and
I. L. Reilly
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 x ∈ X and for i, j = 1,2, i ≠ j, one can assign nbd bases { S(n, i; x) | n = 1, 2,… } such that (i) y ∉ S (n − 1, i; x) imples S(n, i; x) ∩ S (n, j; y) = φ, (ii) y ∈ S (n, i; x) implies S (n, i; y) ⊂ S(n − 1, i; x). We derive two further results from this.

Keywords

quasi-metricquasi-uniformitybitopological space

MSC classification

Secondary: 54E55: Bitopologies
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 2 , April 1988 , pp. 271 - 274
Copyright
Copyright © Australian Mathematical Society 1988

References

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