Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T02:24:22.291Z Has data issue: false hasContentIssue false
  • English
  • Français

Stationary subspaces in ordered spaces

Published online by Cambridge University Press:  17 April 2009

Nobuyuki Kemoto
Nobuyuki Kemoto
Affiliation:
Department of Mathematics, Faculty of Education, Oita University, Dannoharu Oita 870-11, Japan
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.

In this paper, we shall characterise the B(k)-property in generalised ordered (GO) spaces as follows.

For every uncountable regular cardinal K, every GO space has the B(K)-property if and only if it has no closed subspace which is homeomorphic to a stationary set in K (with the subspace topology in K).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 3 , December 1989 , pp. 381 - 387
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Engelking, R., General Topology (PWN-Polish Scientific Publisherers, Warszawa, 1977).Google Scholar
[2]Engelking, R. and Lutzer, D.J., ‘Paracompactness in ordered spaces’, Fund. Math. 94 (1977), 49–58.Google Scholar
[3]Fedorćuk, V.V., ‘Some questions in the theory of ordered spaces’, Siberian Math. J. 10 (1969), 124–132.Google Scholar
[4]Gillman, L. and Henriksen, M., ‘Concerning rings of continuous functions’, Trans. Amer. Math. Soc. 77 (1954), 340–362.Google Scholar
[5]Kemoto, N., ‘The shrinking property and the B-property in ordered spaces’, Fund. Math. (to appear).Google Scholar
[6]Mansfield, M.J., ‘Some generalizations of full normality’, Trans. Amer. Math. Soc. 86 (1957), 443–449.Google Scholar
[7]Navy, K., ‘ParaLindelöfness and paracompactness’. (Thesis, University of Wisconsin, Madison, 1981).Google Scholar
[8]Rudin, M.E., ‘Yasui's questions’, Questions Answers Gen. Topology 1 (1983), 122–127.Google Scholar
[9]Steen, L.A., ‘A direct proof that a linearly ordered space is hereditarily collectionwise normal’, Proc. Amer. Math. Soc. 24 (1970), 727–728.CrossRefGoogle Scholar