Let X be a real or complex vector space equipped with the strongest vector space topology . Besides the result announced in the title we prove that X is uncountable-dimensional if and only if it is not locally pseudoconvex.
@article{bwmeta1.element.bwnjournal-article-apmv66z1p275bwm,
author = {W. \.Zelazko},
title = {The strongest vector space topology is locally convex on separable linear subspaces},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {275-282},
zbl = {0929.46001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p275bwm}
}
W. Żelazko. The strongest vector space topology is locally convex on separable linear subspaces. Annales Polonici Mathematici, Tome 66 (1997) pp. 275-282. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv66z1p275bwm/
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