-metrizable spaces and related matters.
We introduce the structure of a nearness on a -frame and construct the coreflection of the category of nearness -frames to the category of compact regular -frames. This description of the Samuel compactification of a nearness -frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform -frames in [11]. We also construct the uniform coreflection of a nearness -frame, that is, the coreflection of the category of to the category...
We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].
En nous inspirant d’articles de Beardon, nous donnons des résultats concernant les points fixes et les orbites d’auto-applications contractantes et semi-contractantes des espaces connexes localement compacts. Des résultats plus précis sont obtenus dans le cas des variétés complexes Kobayashi hyperboliques.
We define and investigate a generalization of the notion of convex compacta. Namely, for semiconvex combination in a semiconvex compactum we allow the existence of non-trivial loops connecting a point with itself. It is proved that any semiconvex compactum contains two non-empty convex compacta, the center and the weak center. The center is the largest compactum such that semiconvex combination induces a convex structure on it. The convex structure on the weak center does not necessarily coincide...
In this paper semigroups of contractions of metric spaces are considered. The semigroup of contractions of the wreath product of metric spaces is calculated.
The aim of this paper is to introduce and study semi-open sets in biclosure spaces. We define semi-continuous maps and semi-irresolute maps and investigate their behavior. Moreover, we introduce pre-semi-open maps in biclosure spaces and study some of their properties.