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Article

Kąkol, Jerzy
A note on a theorem of Klee. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 34 (1993), issue 1, pp. 79-80
MSC: 46A04, 46A06, 46A10, 46A16, 46B10 | MR 1240205 | Zbl 0799.46007
Keywords:
$F$-spaces; quasi-Banach spaces
Summary:
It is proved that if $E,F$ are separable quasi-Banach spaces, then $E\times F$ contains a dense dual-separating subspace if either $E$ or $F$ has this property.
References:
[1] Day M.M.: The spaces $L^p$ with $0. Bull. Amer. Math. Soc. 46 (1940), 816-823. MR 0002700
[2] Klee V.L.: Exotic Topologies for Linear Spaces. Proc. Symposium on General Topology and its Relations to Modern Algebra, Prague, 1961. MR 0154088 | Zbl 0111.10701
[3] Labuda I., Lipecki Z.: On subseries convergent series and $m$- quasi bases in topological linear spaces. Manuscripta Math. 38 (1982), 87-98. MR 0662771 | Zbl 0496.46006
[4] Lipecki Z.: On some dense subspaces in topological linear spaces. Studia Math. 77 (1984), 413-421. MR 0751762
[5] Rolewicz S.: Metric Linear Spaces. Monografie Mat. 56, PWN, Warszawa, 1972. MR 0438074 | Zbl 0573.46001
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