Locally convex spaces with the strong Gelfand–Phillips property

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.

Symmetric strong vector quasiequilibrium problems in Hausdorff locally convex spaces

* Correspondence: [email protected] Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea Full list of author information is available at the end of the article Abstract In this article, a new symmetric strong vector quasiequilibrium problem in real locally convex Hausdorff topological vector spaces is introduced and studied. An existence theorem ...

Asymmetric locally convex spaces

The aim of the present paper is to introduce the asymmetric locally convex spaces and to prove some basic properties. Among these I do mention the analogs of the EidelheitTuckey separation theorems, of the Alaoglu-Bourbaki theorem on the weak compactness of the polar of a neighborhood of 0, and a Krein-Milman-type theorem. These results extend those obtained by Garcı́a-Raffi et al. (2003) and Co...

Topological Spaces with the Strong Skorokhod Property

We study topological spaces with the strong Skorokhod property, i.e., spaces on which all Radon probability measures can be simultaneously represented as images of Lebesgue measure on the unit interval under certain Borel mappings so that weakly convergent sequences of measures correspond to almost everywhere convergent sequences of mappings. We construct nonmetrizable spaces with such a proper...

Approximate Convexity and Submonotonicity in Locally Convex Spaces