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

Publisher： Cambridge University Press

E-ISSN： 1755-1633|23|1|65-80

ISSN： 0004-9727

Source： Bulletin of the Australian Mathematical Society, Vol.23, Iss.1, 1981-02, pp. : 65-80

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Abstract

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

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