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Characterization of pseudocompactness by the topology of uniform convergence on function spaces

Part of: Fairly general properties Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  09 April 2009

R. A. McCoy
R. A. McCoy
Affiliation:
Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061.
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Abstract

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It is shown that a Tychonoff space X is pseudocompact if and only if for every metrizable space Y, all uniformities on Y induce the same topology on the space of continuous functions from X into Y. Also for certain pairs of spaces X and Y, a necessary and sufficient condition is established in order that all uniformities on Y induce the same topology on the space of continuous functions from X into Y.

Keywords

Function spacestopology of uniform convergenceopen-cover topologypseudocompact.

MSC classification

Secondary: 54C35: Function spaces 54D99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 2 , September 1978 , pp. 251 - 256
Copyright
Copyright © Australian Mathematical Society 1978

References

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