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On the Bitopological Extension of the Bing Metrization Theorem

Part of: Maps and general types of spaces defined by maps Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

Salvador Romaguera  and
Josefa Marín
Salvador Romaguera
Affiliation:
Departmento de MatemáticaPura ETSICCP Universidad Politécnica46022 Valencia, Spain
Josefa Marín
Affiliation:
Departmento de MatemáticaPura ETSICCP Universidad Politécnica46022 Valencia, Spain
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Abstract

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Based on a Junnila's paracompactness characterization we give a definition of pairwise paracompact space which permits us to prove that a bitopological space is quasi-metrizable if, and only if, it is a pairwise developable and pairwise paracompact space. An easy consequence of this result is the biquasi-metric form of the Morita metrization theorem. We also give some results on open mappings and strong quasi-metrics.

Keywords

biquasi-metrizationbitopological spaceopen mappingpairwise developable spacepairwise paracompact spacestrong quasi-metric.

MSC classification

Secondary: 54E35: Metric spaces, metrizability 54E55: Bitopologies 54C10: Special maps on topological spaces (open, closed, perfect, etc.) 54E30: Moore spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 2 , April 1988 , pp. 233 - 241
Copyright
Copyright © Australian Mathematical Society 1988

References

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