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On isocompactness of function spaces

Published online by Cambridge University Press:  17 April 2009

Jiling Cao
Affiliation:
Department of MathematicsThe University of AucklandPrivate Bag 92019AucklandNew Zealand
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Let Cp(X) be the space of all continuous real-valued functions on a Tychonoff space X with the pointwise topology. In this note, we show that if X is a space, then Cp(X) is isocompact. This gives an answer to a recent question of Arkhangel'skii in the class of spaces.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Arkhangel'skii, A., Topological function spaces, Mathematics and its Applications (Kluwer Academic Publishers, Dordrecht, 1992).CrossRefGoogle Scholar
[2]Arkhangel'skii, A.V., ‘On a theorem of Grothendieck in Cp-theory’, Topology Appl. 80 (1997), 2141.CrossRefGoogle Scholar
[3]Bacon, P., ‘The compactness of countably compact spaces’, Pacific J. Math. 32 (1970), 587592.CrossRefGoogle Scholar
[4]Bouziad, A., ‘The Ellis theorem and continuity in groups’, Topology Appl. 50 (1993), 7380.CrossRefGoogle Scholar
[5]Chaber, J., ‘Conditions which imply compactness in countable compact spaces’, Bull. Acad. Polon. Sci. Sér. Sci Math. Astronom. Phys. 24 (1976), 993998.Google Scholar
[6]Engelking, R., General topology (Polish Scientific Publisher, Warszawa, 1977).Google Scholar
[7]Gruenhage, C., ‘Infinite games and generalizations of first-countable spaces’, General Topology and Appl. 6 (1976), 339352.CrossRefGoogle Scholar
[8]Michael, E., ‘A note on closed maps and compact sets’, Israel J. Math. 2 (1964), 173176.CrossRefGoogle Scholar
[9]Nedev, S., ‘Symmetrizable spaces and final compactness’, Soviet Math. Dokl. 8 (1967), 890892.Google Scholar
[10]Worrell, J. Jr and Wicke, H., ‘Characterizations of developable topological spaces’, Canad. J. Math. 17 (1965), 820830.CrossRefGoogle Scholar