On -metrizable spaces
On sequence-covering --images of locally separable metric spaces
On shapes of topological spaces
On Simultaneous Fixed Points of Multi-Valued Maps.
On some covering properties of metric spaces
On some metrizations of the hyperspace of compact sets
On some properties of hyperconvex spaces.
On some properties of proximity in metric spaces
On some property of the tangency relation of sets.
On some subspaces of the Helly space
On spaces with point-countable -systems
This paper deals with the behavior of -spaces, countably bi-quasi--spaces and singly bi-quasi--spaces with point-countable -systems. For example, we show that every -space with a point-countable -system is locally compact paracompact, and every separable singly bi-quasi--space with a point-countable -system has a countable -system. Also, we consider equivalent relations among spaces entried in Table 1 in Michael’s paper [15] when the spaces have point-countable -systems.
On special metrics characterizing topological properties
On subcompactness and countable subcompactness of metrizable spaces in ZF
We show in ZF that: (i) Every subcompact metrizable space is completely metrizable, and every completely metrizable space is countably subcompact. (ii) A metrizable space is countably compact if and only if it is countably subcompact relative to . (iii) For every metrizable space , the following are equivalent: (a) is compact; (b) for every open filter of , ; (c) is subcompact relative to . We also show: (iv) The negation of each of the statements, (a) every countably subcompact metrizable...
On Szymański theorem on hereditary normality of
We discuss the following result of A. Szymański in “Retracts and non-normality points" (2012), Corollary 3.5.: If is a closed subspace of and the -weight of is countable, then every nonisolated point of is a non-normality point of . We obtain stronger results for all types of points, excluding the limits of countable discrete sets considered in “Some non-normal subspaces of the Čech–Stone compactification of a discrete space" (1980) by A. Błaszczyk and A. Szymański. Perhaps our proofs...
On the curvature of nonregular saddle surfaces in the hyperbolic and spherical three-space.
On the density of the hyperspace of a metric space
We calculate the density of the hyperspace of a metric space, endowed with the Hausdorff or the locally finite topology. To this end, we introduce suitable generalizations of the notions of totally bounded and compact metric space.
On the extensions of uniformly continuous mappings
On the fundamental group of the fixed points of an unipotent action.
On the gluing of hyperconvex metrics and diversities
In this work we consider two hyperconvex diversities (or hyperconvex metric spaces) (X, δX) and (Y, δY ) with nonempty intersection and we wonder whether there is a natural way to glue them so that the new glued diversity (or metric space) remains being hyperconvex. We provide positive and negative answers in both situations.
On the inverse image of Baire spaces.