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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

[1]Köthe, G., Topological vector spaces I (Springer-Verlag, 1969).Google Scholar
[2]Lacey, H. E., ‘Separable quotients of Banach spaces’, An. Acad. Brasil. Cienc. 44 (1972), 185–189.Google Scholar
[3]Robertson, W. J. and Narayanaswami, P. P., On properly separable quotients and barrelled spaces, (Department of Mathematics, The University of Western Australia, Research Report, 03 1988/1).Google Scholar
[4]Robertson, A. P. and Robertson, W. J., Topological vector spaces, 2nd ed. (Cambridge University Press, 1973).Google Scholar
[5]Saxon, S. A. and Wilansky, A., ‘The equivalence of some Banach space problems’, Colloq. Math. 37 (1977), 217–226.Google Scholar