Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T10:28:06.575Z Has data issue: false hasContentIssue false

On subparacompact and countably subparacompact spaces

Published online by Cambridge University Press:  17 April 2009

M.K. Singal
Affiliation:
Institute of Advanced Studies, Meerut University, Meerut, India.
Pushpa Jain
Affiliation:
Maitreyi College, Delhi University, Delhi, India.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A space is said to be subparacompact if every open covering of it has a σ-discrete closed refinement. Subparacompactness is equivalent to Fσ -screenability of McAuley and also to σ-paracompactness of Arhangel'skiĭ. Some properties of these spaces have been obtained in this note. Countably subparacompact spaces, which can be defined in an analogous manner, have also been studied.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Arhangel'skiĭ, A.V., “Mappings and spaces” (Russian), Uspehi Mat. Nauk 21 (1966), no. 4 (130), 133184; translated as Russian Math. Surveys 21 (1966), no. 4, 115162.Google Scholar
[2]Bing, R.H., “Metrization of topological spaces”, Canad. J. Math. 3 (1951), 175186.CrossRefGoogle Scholar
[3]Burke, Dennis K., “On subparacompact spaces”, Proc. Amer. Math. Soc. 23 (1969), 655663.CrossRefGoogle Scholar
[4]Burke, Dennis K., “Subparacompact spaces”, Proc. Washington State Univ. Conf. General Topology, Washington, 1970, 3949. (Edited and distributed by Pullman, Pi Mu Epsilon; Department of Mathematics, Washington State University, 1970.)Google Scholar
[5]Burke, D. K. and Stoltenberg, R. A., “A note on p-spaces and Moore spaces”, Pacific J. Math. 30 (1969), 601608.CrossRefGoogle Scholar
[6]Čoban, M. M., “σ-paracompact spaces” (Russian), Vestnik Moskov. Univ. Ser. I Mat. Meh. 24 (1969), no. 1, 2027.Google Scholar
[7]Dowker, C. H., “Inductive dimension of completely normal spaces”, Quart. J. Math. Oxford (2) 4 (1953), 267281.CrossRefGoogle Scholar
[8]Hodel, R. E., “Sum theorems for topological spaces”, Pacific J. Math. 30 (1969), 5965.CrossRefGoogle Scholar
[9]Hodel, R. E., “A note on subparacompact spaces”, (to appear).Google Scholar
[10]Katuta, Yûkiti, “A theorem on paracompactness of product spaces”, Proc. Japan Acad. 43 (1967), 615–618.Google Scholar
[11]Mansfield, M. J., “On countably paracompact normal spaces”, Canad. J. Math. 9 (1957), 443449.CrossRefGoogle Scholar
[12]McAuley, Louis F., “A note on complete collectionwise normality and paracompactness”, Proc. Amer. Math. Soc. 9 (1958), 796799.Google Scholar
[13]Singal, M. K. and Arya, Shashi Prabha, “Two sum theorems for topological spaces”, Israel J. Math. 8 (1970), 155158.CrossRefGoogle Scholar