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A Cellular Constraint in Supercompact Hausdorff Spaces

Published online by Cambridge University Press:  20 November 2018

Murray G. Bell
Murray G. Bell*
Affiliation:
University of Alberta, Edmonton, Alberta.
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In this paper we prove a cardinal inequality for supercompact Uausdorff spaces which gives insight into the cellular structure of such spaces and yields new examples of compact Uausdorff non-supercompact spaces.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1144 - 1151
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Bell, M. G., Not all compact Hausdorff spaces arc supercompact, to appear, Gen. Topology Appl. (1977).Google Scholar
2. Brouwer, A. E. and Schrijver, A., A characterization of supercompactness with an application to tree-like spaces, Report Mathematical Centre ZW o4/74, Amsterdam (1974).Google Scholar
3. van Donwen, K., Special bases in compact metrizahle spaces, manuscript.Google Scholar
4. van Donwen, K. and van Mill, J., Supercompact spaces, Rapport 40, Wiskundig Seminarian! 1er Yrije Iniversiteit, Amsterdam (1970).Google Scholar
5. van Donwen, K. and Pryzymusinski, T. C., Separable extensions of first countable spaces, to appear.Google Scholar
6. de Groot, J., Supercompactness and superextensions, Proc. I. Intcrni. Symp. on Extension theory of Topological Structures (YEB Deutscher Yerlag YYiss, Berlin 1969), 89–90.Google Scholar
7. Michael, E., Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152–18.Google Scholar
8. van Mill, J., On supercompactness and superextensions, Rapport -i?, Wiskundig Seminarium 1er Yrije Universiteit, Amsterdam (1975).Google Scholar
9. van Mill, J., A topological characterization of products of compact tree-like spaces, Rapport (Wiskundig Seminarium der Yrije Iniversiteit, Amsterdam, 1975).Google Scholar
10. Rudin, M. E., Lectures on set theoretic topology, Regional Conf. Ser. in Math., Providence, R.I., Amer. Math. Soc. £,; (1975).Google Scholar
11. Strok, M. and Szymânski, A., Compact metric spaces have binary bases, Fund. Math. 80 (1975), 81–91.Google Scholar
12. Verbeek, A., Superextensions of topological spaces, Math. Centre Tracts (1972).Google Scholar
13. Yietoris, L., Bereiche Zwciter Ordnung, Monatshefte fiir Mathematik unci Physik (1923), 49–62.Google Scholar
14. Willard, S., General topology (Addison-Wesley Publishing Co., Reading, Mass., 1970).Google Scholar