Characterizations of metrizable topological vector spaces and their asymmetric generalizations in terms of fuzzy (quasi-)norms
We obtain characterizations of those paratopological vector spaces that are quasi-metrizable, locally bounded, quasi-metrizable locally convex, and quasi-normable, respectively, in terms of appropriate kinds of fuzzy quasi-norms. Characterizations of distinguished kinds of metrizable topological vector spaces, some of them known already, are deduced as particular cases of our approach. (C) 2010 Elsevier B.V. All rights reserved.
paratopological vector space locally bounded locally convex fuzzy quasi-norm fuzzy norm fuzzy quasi-metric quasi-normable