Hostname: page-component-77c89778f8-vsgnj Total loading time: 0 Render date: 2024-07-16T11:37:29.654Z Has data issue: false hasContentIssue false
  • English
  • Français

On irreducible spaces

Published online by Cambridge University Press:  17 April 2009

James R. Boone
James R. Boone
Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas, USA.
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 constructive proof of a theorem of Worrell and Wicke, which states that every open covering of a θ-refinable space has a σ-distributively point-finite open refinement that covers the space minimally, is presented. Spaces for which every open covering has an open refinement which covers the space minimally are characterized by the use of discrete closed collections and some open questions relating to spaces of this type are included.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1975 , pp. 143 - 148
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Arens, Richard and Dugundji, J., “Remark on the concept of compactness”, Portugal. Math. 9 (1950), 141–143.Google Scholar
[2]Bennett, H.R. and Lutzer, D.J., “A note on weak θ-refinability”, General Topology and Appl. 2 (1972), 49–54.CrossRefGoogle Scholar
[3]Boone, James R., “A characterization of metacompactness in the class of θ-refinable spaces”, General Topology and Appl. 3 (1973), 253–264.CrossRefGoogle Scholar
[4]Boone, James R., “An example relating to Arhangel'skii's class MOBI”, Proc. Amer. Math. Soc. 41 (1973), 615–618.Google Scholar
[5]Burke, Dennis K., “A note on R.H. Bing's Example G”, Topology Conference, 47–52 (Proc. Conf. Virginia Polytechnic Institute and State University, 1973. Lecture Notes in Mathematics, 375. Springer-Verlag, Berlin, Heidelberg, New York, 1974).Google Scholar
[6]Christian, Upton J., “A note on the relation between Lindelöf and ℵ1-compact spaces”, Comment. Math. Prace Mat. 16 (1972), 215–217.Google Scholar
[7]Christian, U.J., “Concerning certain minimal cover refinable spaces”, Fund. Math. 76 (1972), 213–222.CrossRefGoogle Scholar
[8]Worrell, J.M. Jr and Wicke, H.H., “Characterizations of developable topological spaces”, Canad. J. Math. 17 (1965), 820–830.CrossRefGoogle Scholar