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Necessary and sufficient conditions for precompact sets to be metrisable

Published online by Cambridge University Press:  17 April 2009

J.C. Ferrando ,
J. Kasakol  and
M. López Pellicer
J.C. Ferrando
Affiliation:
Centro de Investigación Operativa, Universidad Miguel Hernández, E-03202 Elche (Alicante), Spain, e-mail: jc.ferrando@umh.es
J. Kasakol
Affiliation:
Faculty of Mathematics and Informatics, A. Mickiewicz University, 61-614 Poznań, Poland, e-mail: Kakol@amu.edu.pl
M. López Pellicer
Affiliation:
Departamento de Matemática Aplicada and IMPA, Universidad Politécnica, E-46022 Valencia, Spain, e-mail: mlopezpe@mat.upv.es
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This self-contained paper characterises those locally convex spaces whose (weakly) precompact (respectively, compact) subsets are metrisable. Applications and examples are provided. Our approach also applies to get Cascales-Orihuela's, Valdivia's and Robertson's metrisation theorems for (pre)compact sets.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 1 , August 2006 , pp. 7 - 13
Copyright
Copyright © Australian Mathematical Society 2006

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