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A note on order paracompactness

Published online by Cambridge University Press:  17 April 2009

M.K. Singal  and
Shashi Prabha Arya
M.K. Singal
Affiliation:
Institute of Advanced Studies, Meerut University, India
Shashi Prabha Arya
Affiliation:
Faculty of Mathematics, University of Delhi, India.
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Abstract

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This paper contains some results on order paracompact spaces. Some of the results offer improvements of some of the results of McCandless in Canad. J. Math. 21 (1969). Some other results of McCandless are deduced as corollaries from our results. The concepts of order closure preserving and order cushioned collections are introduced and using these, characterizations of paracompactness in regular spaces are obtained.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 2 , April 1971 , pp. 273 - 279
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Bing, R.H., “Metrization of topological spaces”, Canad. J. Math. 3 (1951), 175–186.CrossRefGoogle Scholar
[2]Fitzpatrick, Ben Jr, and Ford, Ralph M., “On the equivalence of small and large inductive dimension in certain metric spaces”, Duke Math. J. 34 (1967), 33–37.CrossRefGoogle Scholar
[3]Katuta, Yûkiti, “A theorem on paracompactness of product spaces”, Proc. Japan Acad. 43 (1967), 615–618.Google Scholar
[4]McCandless, Bryon H., “On order paracompact spaces”, Canad. J. Math. 21 (1969), 400–405.CrossRefGoogle Scholar
[5]Michael, Ernest, “A note on paracompact spaces”, Proc. Amer. Math. Soc. 4 (1953), 831–838.CrossRefGoogle Scholar
[6]Michael, E., “Yet another note on paracompact spaces”, Proc. Amer. Math. Soc. 10 (1959), 309–314.CrossRefGoogle Scholar
[7]Tamano, Hisahiro, “On paracompactness”, Pacific J. Math. 10 (1960), 1043–1047.CrossRefGoogle Scholar
[8]Vaughan, Jerry E., “Linearly ordered collections and paracompactness”, (to appear).Google Scholar