On spaces whose product with every Lindelöf space is Lindelöf
On spaces with the property of weak approximation by points
A sufficient condition that the product of two compact spaces has the property of weak approximation by points (briefly WAP) is given. It follows that the product of the unit interval with a compact WAP space is also a WAP space.
On -starcompact spaces.
On -starcompact spaces
A space is -starcompact if for every open cover of there exists a Lindelöf subset of such that We clarify the relations between -starcompact spaces and other related spaces and investigate topological properties of -starcompact spaces. A question of Hiremath is answered.
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 pseudo-radial spaces
It is proved that, under the Martin’s Axiom, every -space with countable tightness is a subspace of some pseudo-radial space. We also give several characterizations of subspaces of pseudo-radial spaces and conclude that being a subspace of a pseudo-radial space is a local property.
On subspaces of the Pixley-Roy example
On supercomplete uniform spaces IV: Countable products
On supercomplete uniform spaces V: Tamano's product problem
On symmetric products
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 2-homogeneity of Cartesian products
On the cardinality of power homogeneous Hausdorff spaces
We prove that the cardinality of power homogeneous Hausdorff spaces X is bounded by . This inequality improves many known results and it also solves a question by J. van Mill. We further introduce Δ-power homogeneity, which leads to a new proof of van Douwen’s theorem.
On the category of topological topologies
On the class of all spaces of weight not greater than ω_1 whose Cartesian product with every Lindelöf space is Lindelöf
On the co-completeness of the category of Hausdorff uniform spaces.
On the Compactness and Countable Compactness of in ZF
In the framework of ZF (Zermelo-Fraenkel set theory without the Axiom of Choice) we provide topological and Boolean-algebraic characterizations of the statements " is countably compact" and " is compact"
On the construction of the extensional topological hull
On the deficiency of product spaces
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.