Abstract
SynopsisIn 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.
Publisher
Cambridge University Press (CUP)
Cited by
14 articles.
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2. A Biased View of Topology as a Tool in Functional Analysis;Recent Progress in General Topology III;2013-12-12
3. Overview;Descriptive Topology in Selected Topics of Functional Analysis;2011
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5. Necessary and sufficient conditions for precompact sets to be metrisable;Bulletin of the Australian Mathematical Society;2006-08