Carmen Alegre

On the Hahn-Banach Theorem in Certain Linear Quasi-uniform Structures

A Hahn-Banach type theorem in the frame of quasi-normed spaces (a class of linear spaces with a quasi-uniform structure that contains all linear lattices) is given. The classical result for positive functionals follows as a particular case.

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.

On a class of real normed lattices

AbstractWe say that a real normed lattice is quasi-Baire if the intersection of each sequence of monotonic open dense sets is dense. An example of a Baire-convex space, due to M. Valdivia, which is not quasi-Baire is given. We obtain that E is a quasi-Baire space iff

A fixed point theorem for generalized contractions involving w-distances on complete quasi-metric spaces

(E,T(\mathcal{U}),T((\mathcal{U}^{ - 1} ))

A note on φ-contractions in probabilistic and fuzzy metric spaces

is a pairwise Baire bitopological space, where

The Hahn-Banach Extension Theorem for Fuzzy Normed Spaces Revisited

\mathcal{U}