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The metrisability of precompact sets

Published online by Cambridge University Press:  17 April 2009

Neill Robertson
Neill Robertson
Affiliation:
Department of Mathematics, University of Cape Town, Rondebosch 7700, South Africa
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Abstract

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A uniform space is trans-separable if every uniform cover has a countable subcover. We show that a uniform space is trans-separable if it contains a suitable family of precompact sets. Applying this result to locally convex spaces, we are able to deduce that the precompact subsets of a wide class of spaces are metrisable. The proof of our main Theorem is based on a cardinality argument, and is reminiscent of the classical Bolzano-Weierstrass Theorem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 1 , February 1991 , pp. 131 - 135
Copyright
Copyright © Australian Mathematical Society 1991

References

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