Quasi-barrelled Locally Convex Spaces

P-adic Spaces of Continuous Functions II

Necessary and sufficient conditions are given so that the space C(X, E) of all continuous functions from a zero-dimensional topological space X to a nonArchimedean locally convex space E, equipped with the topology of uniform convergence on the compact subsets of X, to be polarly absolutely quasi-barrelled, polarly אo-barrelled, polarly `∞-barrelled or polarly co-barrelled. Also, tensor product...

Approximate Convexity and Submonotonicity in Locally Convex Spaces

Topological number for locally convex topological spaces with continuous semi-norms

In this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. It gives some criterions to study locally convex topological spaces in a discrete approach.

Lipschitz Properties of Convex Mappings

The present paper is concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex subset Ω of a locally convex space X and taking values in a locally convex space Y ordered by a normal cone. One proves also equi-Lipschitz properties for pointwise bounded families of continuous convex mappings, provided the source space X is barr...

On the dual of certain locally convex function spaces

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.