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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
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Abstract

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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

Information

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