On paracompactness in function spaces with the compact-open topology.

Author:
Paul O’Meara

Journal:
Proc. Amer. Math. Soc. **29** (1971), 183-189

MSC:
Primary 54.28

DOI:
https://doi.org/10.1090/S0002-9939-1971-0276919-3

MathSciNet review:
0276919

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Abstract | References | Similar Articles | Additional Information

Abstract: A *k-network* for a space *X* is a family of subsets of *X* such that if , with *C* compact and *U* open, then there is a finite union *R* of members of such that . An -*space* is a -space having a countable *k*-network and an -*space* is a -space having a -locally finite *k*-network. In this paper, it is shown that if *X* is an -space and *Y* is a paracompact -space, then , with the compact-open topology is a paracompact -space. The result implies that if *X* is separable metric and *Y* is metric, then is paracompact.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1971-0276919-3

Keywords:
Function spaces,
compact-open topology,
paracompact,
-locally finite family,
*k*-network,
network,
-space,
-space,
-space,
compact-covering mapping,
separable metric space,
metric space

Article copyright:
© Copyright 1971
American Mathematical Society