On subsets of Alexandroff duplicates
We characterize the subsets of the Alexandroff duplicate which have a G-diagonal and the subsets which are M-spaces in the sense of Morita.
On subspaces of measurable real functions.
On subspaces of separable first countable -spaces
On subspaces of the Pixley-Roy example
On supercomplete uniform spaces. II
On supercomplete uniform spaces IV: Countable products
On supercomplete uniform spaces V: Tamano's product problem
On symmetric generalized uniform spaces
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 Telgársky's question concerning β-favorability of the strong Choquet game
Answering a question of Telgársky in the negative, it is shown that there is a space which is β-favorable in the strong Choquet game, but all of its nonempty -subspaces are of the second category in themselves.
On the category number of topological spaces.
On the classification of locally compact separable metric spaces
On the co-completeness of the category of Hausdorff uniform spaces.
On the complexity of Hamel bases of infinite-dimensional Banach spaces
We call a subset S of a topological vector space V linearly Borel if for every finite number n, the set of all linear combinations of S of length n is a Borel subset of V. It is shown that a Hamel basis of an infinite-dimensional Banach space can never be linearly Borel. This answers a question of Anatoliĭ Plichko.
On the concepts of balls in a -metric space.
On the convergence of certain sequences and some applications
On the curvature of nonregular saddle surfaces in the hyperbolic and spherical three-space.
On the definition of a probalistic normed 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 differentiation theorem in metric groups