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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.

Information

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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