J Austral Math Soc Ser A 47 pp307--312, 1989.

On Properly Separable Quotients of Strict (LF) Spaces

W. J. Robertson

Abstract

All known Banach spaces have an infinite-dimensional separable quotient and so do all non-normable 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 matrisable 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.

1980 AMS Subject Classification (1985 Revision): 46A05, 46A07, 46A12

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Authors

W. J. Robertson

Department of Mathematics, University of Western Australia, Nedlands, W. A. 6009, Australia.