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.
@article{118557, author = {Jerzy K\k akol}, title = {A note on a theorem of Klee}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {34}, year = {1993}, pages = {79-80}, zbl = {0799.46007}, mrnumber = {1240205}, language = {en}, url = {http://dml.mathdoc.fr/item/118557} }
Kąkol, Jerzy. A note on a theorem of Klee. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 79-80. http://gdmltest.u-ga.fr/item/118557/
The spaces $L^p$ with $0 , Bull. Amer. Math. Soc. 46 (1940), 816-823. (1940)
| MR 0002700
Exotic Topologies for Linear Spaces, Proc. Symposium on General Topology and its Relations to Modern Algebra, Prague, 1961.
| MR 0154088
| Zbl 0111.10701
On subseries convergent series and $m$- quasi bases in topological linear spaces, Manuscripta Math. 38 (1982), 87-98. (1982)
| MR 0662771
| Zbl 0496.46006
On some dense subspaces in topological linear spaces, Studia Math. 77 (1984), 413-421. (1984)
| MR 0751762
Metric Linear Spaces, Monografie Mat. 56, PWN, Warszawa, 1972.
| MR 0438074
| Zbl 0573.46001