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Metrizable (LF)-spaces, (db)-spaces, and the separable quotient problem

Published online by Cambridge University Press:  17 April 2009

Stephen A. Saxon  and
P.P. Narayanaswami
Stephen A. Saxon
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32611, USA
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Abstract

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The existence of metrizable (LF)-spaces was announced by Stephen A. Saxon (“Metrizable generalized (LF)-spaces”, 701–46–14), in Notices Amer. Math. Soc. 20 (1973), A–143. Elsewhere, the authors have discovered an abundant existence of metrizable and normable (generalized) (LF)-spaces, while observing that an (LF)-space is metrizable if and only if it is Baire-like. Recently, W. Robertson, I. Tweddle and F.E. Yeomans introduced the class of locally convex spaces E having the property

(db) if E is the union of an increasing sequence (En) of vector subspaces, then some En is dense and barrelled.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1981 , pp. 65 - 80
Copyright
Copyright © Australian Mathematical Society 1981

References

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