Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T18:42:27.317Z Has data issue: false hasContentIssue false
  • English
  • Français

Compact Sets in CP(X) and Calibers

Published online by Cambridge University Press:  20 November 2018

N. D. Kalamidas  and
G. D. Spiliopoulos
N. D. Kalamidas
Affiliation:
Department of Mathematics University of Athens GR-15781 Panepistimiopolis Athens, Greece
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.

This presentation concerns the relation of chain conditions on a space X, with the weights of compact sets in Cp(X), generalizing up to the class of dσ-bounded spaces, or stable spaces. In the last case, stronger results are obtained for Corson compact subsets of CP(X).

Keywords

54C4054A2554C35caliberpoint finite cellularitysupersequencestabilitymonolithicityCorson compactpseudocompactBanach spaceŠhanin numberspreadtightness
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 4 , 01 December 1992 , pp. 497 - 502
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Arkhangel'skii, A. V., A survey on Cp-theory, Q and A in General Topology, 5(1987), Special Issue.Google Scholar
2. Arkhangel'skii, A. V. and Tkachuk, V. V., Calibers and point finite cellularity of the space Cp﹛X) and some questions ofS. Gul'ko andM. Husek, Topology and its applications 23(1986), 63–73.Google Scholar
3. Arkhangel'skii, A. V., Function spaces in the topology ofpointwise convergence, and compact sets, Russian Math. Surveys (5) 39(1984), 9–56.Google Scholar
4. Arkhangel'skii, A. V., Topological properties of function spaces: Duality theorems, Soviet Math. Dokl. (2) 27(1983), 470–473.Google Scholar
5. Gul'ko, S. R, On the structure of spaces of continuous functions and their complete paracompactness, Russian Math. Surveys (6) 34(1979), 36–44.Google Scholar
6. Comfort, W. W. and Negrepontis, S., Chain Conditions in Topology, Cambridge University Press, 1982.Google Scholar
7. Juhasz, I., Cardinal functions in Topology—Ten years later, Math. Centrum, Amsterdam, 1980.Google Scholar
8. Tkachuk, V. V., Calibers of spaces of Junctions and the metrization problem for compact subsets ofCp(X), Vestnik Moskovskogo Universiteta Matematika (3) 43(1988), 21–24.Google Scholar
9. Tkachuk, V. V., The smallest subring of the ring Cp(Cp(X)) containing X∪{1} is everywhere dense in Cp(Cp(X)), Vestnik Moskovskogo Universiteta Matematika (1) 42(1987), 20–23.Google Scholar