Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-04T19:30:01.521Z Has data issue: false hasContentIssue false
  • English
  • Français

Paracompactness in Locally Lindelöf Spaces

Published online by Cambridge University Press:  20 November 2018

Zoltán Balogh
Zoltán Balogh*
Affiliation:
Kossuth University, Debrecen, Hungary
Rights & Permissions [Opens in a new window]

Extract

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.

This paper contains a set of results concerning paracompactness of locally nice spaces which can be proved by (variations on) the technique of “stationary sets and chaining” combined with other techniques available at the present stage of knowledge in the field. The material covered by the paper is arranged in three sections, each containing, in essence, one main result.

The main result of Section 1 says that a locally Lindelöf, submeta-Lindelöf ( = δθ-refinable) space is paracompact if and only if it is strongly collectionwise Hausdorff. Two consequences of this theorem, respectively, answer a question raised by Tall [7], and strengthen a result of Watson [9]. In the last two sections, connected spaces are dealt with. The main result of the second section can be best understood from one of its consequences which says that under 2ωl > 2ω, connected, locally Lindelöf, normal Moore spaces are metrizable.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 3 , 01 June 1986 , pp. 719 - 727
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Alster, K. and Pol, R., Moore spaces and the collectionwise Hausdorff property, Bull. Acad. Polon. Sci. Ser. Sci. Mat. Astronom. 23, 1189–1192.Google Scholar
2. Devlin, J. K. and Shelah, S., A note on the normal Moore space conjecture, Can. J. Math. 31 (1979), 241–251.Google Scholar
3. Fleissner, W. G., Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294–298.Google Scholar
4. Gruenhage, G., Paracompactness in normal, locally connected, locally compact spaces, Top. Proc. 4 (1979), 393–405.Google Scholar
5. Junnila, H., Three covering properties, in: Surveys in general topology (Academic Press, 1980), 195–245.CrossRefGoogle Scholar
6. Tall, F., Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems, Dissertationes Mathematicae (Rozpravry Matematyczne) 148 (1977).Google Scholar
7. Tall, F., When are normal, locally compact spaces collectionwise normal?, preprint.Google Scholar
8. Taylor, A. D., Diamond principles, ideals and the normal Moore space problem, Can. J. Math. 33 (1981), 282–296.Google Scholar
9. Watson, S., Locally compact normal spaces in the constructible universe, Can. J. Math. 34 (1982), 1091–1096.Google Scholar
10. Worrel, J. M. Jr., Locally separable Moore spaces, in: Set-theoretic topology (Academic Press, New York, 1977), 413–436.CrossRefGoogle Scholar