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Metrizability of precompact subsets in (LF)-spaces

Published online by Cambridge University Press:  14 November 2011

B. Cascales  and
J. Orihuela
B. Cascales
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Murcia, 30.001-Murcia, Spain
J. Orihuela
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Murcia, 30.001-Murcia, Spain
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Synopsis

In this paper we prove that every precompact subset in any (LF)-space has a metrizable completion. As a consequence every (LF)-space is angelic and in this way the answer to a question posed by K. Floret [3] is given. Some contributions to the general problem of regularity in inductive limits posed by K. Floret [3] are also given. Particularly, extensions of well-known results of H. Neuss and M. Valdivia are provided in the general setting of (LF)-spaces. It should also be noted that our results hold for inductive limits of an increasing sequence of metrizable spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 3-4 , 1986 , pp. 293 - 299
Copyright
Copyright © Royal Society of Edinburgh 1986

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