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A new bitopological paracompactness

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 Mathematics, University of Auckland, Auckland, New Zealand
I. L. Reilly
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand
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Abstract

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In this paper we define generalization of paracompactness for bitopological spaces. (X, τ1, τ2) is Δ-pairwise paracompact if and only if every τi open cover admits a τ1 ∨ τ2 open refinement which is τ1 ∨ τ2 locally finite. Every quasimetric space (X, τp, τq) is Δ-pairwise paracompact. An analogue of Michael's characterization of regular paracompact spaces is proved for Δ-pairwise paracompact spaces.

MSC classification

Secondary: 54E55: Bitopologies
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 2 , October 1986 , pp. 268 - 274
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Cooke, I. E. and Reilly, I. L., ‘On bitopological compactness’, J. London Math. Soc. (2) 13 (1975), 518–522.Google Scholar
[2]Dugundji, J., Topology (Allyn and Bacon, Boston, Mass., 1966).Google Scholar
[3]Fletcher, P., Hoyle, H. B. III and Patty, C. W., ‘The comparison of topologies’, Duke Math. J. 36 (1969), 325–332.Google Scholar
[4]Kelley, J. L., General topology (Van Nostrand, New Jersey, 1955).Google Scholar
[5]Kelly, J. C., ‘Bitopological spaces’, Proc. London Math. Soc. 13 (1963), 71–89.Google Scholar
[6]Raghavan, T. G. and Reilly, I. L., ‘Metrizability of quasimetric spaces’, J. London Math. Soc. (2) 15 (1977), 169–172.CrossRefGoogle Scholar
[7]Raghavan, T. G. and Reilly, I. L., ‘On nonsymmetric topological structres’ (Topology (Proc. Fourth Colloq., Budapest, 1978) Vol. II, Colloq. Math. Soc. Janos Bolyai, Vol. 23, North-Holland, Amsterdam, 1980, pp. 1005–1014).Google Scholar
[8]Sion, M. and Zelmer, G., ‘On quasimetrizability’, Canad. J. Math. 19 (1967), 1243–1249.Google Scholar
[9]Stoltenberg, R. A., ‘On quasimetric spaces’, Duke Math. J. 36 (1969), 65–71.Google Scholar
[10]Wilson, W. A., ‘On quasimetric spaces’, Amer. J. Math. 53 (1931), 675–684.Google Scholar