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Characterization of pseudocompactness by the topology of uniform convergence on function spaces
Published online by Cambridge University Press: 09 April 2009
Abstract
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.
MSC classification
- 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
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