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On properly separable quotients of strict (LF) Spaces

Published online by Cambridge University Press:  09 April 2009

W. J. Robertson
W. J. Robertson
Affiliation:
Department of Mathematics, University of Western Australia Nedlands, W. A. 6009, Australia
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Abstract

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All known Banach spaces have an infinite-dimensional separable quotient and so do all nonnormable Fréchet spaces, although the general question for Banach spaces is still open. A properly separable topological vector space is defined, in such a way that separable and properly separable are equivalent for an infinite-dimensional complete metrisable space. The main result of this paper is that the strict inductive limit of a sequence of non-normable Fréchet spaces has a properly separable quotient.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 2 , October 1989 , pp. 307 - 312
Copyright
Copyright © Australian Mathematical Society 1989

References

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