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Two characterizations of quasi-pseudometrizable bitopological spaces

Part of: Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

S. Romaguera
S. Romaguera
Affiliation:
Departmento de Matemáticas II ETSICCPUniversidad PolitécnicaValencia-22, Spain
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Abstract

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By using pairwise relatively complete families of functions, which we define here, we obtain two characterizations of quasi-pseudometrizable bitopological spaces from which some known theorems can be derived as easy corollaries.

Keywords

bitopological spacesquasi-pseudometrization.

MSC classification

Secondary: 54E55: Bitopologies 54E35: Metric spaces, metrizability
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 3 , December 1983 , pp. 327 - 333
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Fletcher, P., Hoyle, H. B. III and Patty, C. W., ‘The comparison of topologies’, Duke Math. J. 36 (1969), 325–331.CrossRefGoogle Scholar
[2]Guthrie, J. A. and Henry, M., ‘Metrization, paracompactness and real-valued functions’, Fund. Math. 95 (1977), 49–53.CrossRefGoogle Scholar
[3]Guthrie, J. A. and Henry, M., ‘Metrization, paracompactness and real-valued functions II’, Fund. Math. 96 (1979), 13–20.CrossRefGoogle Scholar
[4]Kelly, J. C., ‘Bitopological spaces’, Proc. London Math. Soc. 13 (1963), 71–89.CrossRefGoogle Scholar
[5]Lane, E. P., ‘Bitopological spaces and quasi-uniform spaces’, Proc. London Math. Soc. 17 (1967), 241–256.CrossRefGoogle Scholar
[6]Pareek, C. M., ‘Bitopological spaces and quasi-metric spaces’, J. Univ. Kuwait Sci. 6 (1980), 1–7.Google Scholar
[7]Patty, C. W., ‘Bitopological spaces’, Duke Math. J. 34 (1967), 387–392.CrossRefGoogle Scholar
[8]Reilly, I. L., ‘Quasi-gauge spaces’, J. London Math. Soc. 6 (1973), 481–487.CrossRefGoogle Scholar
[9]Ribeiro, H., ‘Sur les éspaces á métrique faible’, Portugal. Math. 4 (1943), 21–40.Google Scholar
[10]Romaguera, S., ‘On bitopological quasi-pseudometrization’, J. Austral. Math. Soc., to appear.Google Scholar
[11]Salbany, S., ‘Quasi-metrization of bitopological spaces’, Arch. Math. 23 (1972), 299–306.CrossRefGoogle Scholar
[12]Stoltenberg, R. A., ‘On quasi-metric spaces’, Duke Math. J. 36 (1969), 65–72.CrossRefGoogle Scholar