On spaces whose denumerable subspaces are discrete
On spaces with the ideal convergence property
Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.
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 stratifiable fuzzy topological spaces
The aim of the paper is to extend the notion of stratifiability from the category Top of topological spaces to the category CFT of [Chang] fuzzy topological spaces and to develop the corresponding theory.
On strong convergence of multivalued maps
On strong form of Arzela convergence.
On sub-, pseudo- and quasimaximal spaces
The structure of sub-, pseudo- and quasimaximal spaces is investigated. A method of constructing non-trivial quasimaximal spaces is presented.
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 summability in convergence -groups
On supertightness and function spaces
On surjective kernels of partial algebras.
On the absoluteness of openly-generated and Dugundji spaces
On the almost Lindelöf property in products of separable metric spaces
On the associated locally connected space.
On the axioms preserved by modifications of topologies without axioms
On the cardinality and weight spectra of compact spaces, II
Let B(κ,λ) be the subalgebra of P(κ) generated by . It is shown that if B is any homomorphic image of B(κ,λ) then either or ; moreover, if X is the Stone space of B then either or . This implies the existence of 0-dimensional compact spaces whose cardinality and weight spectra omit lots of singular cardinals of “small” cofinality.
On the cardinality of functionally Hausdorff spaces
In this paper two new cardinal functions are introduced and investigated. In particular the following two theorems are proved: (i) If is a functionally Hausdorff space then ; (ii) Let be a functionally Hausdorff space with . Then there is a subset of such that and .
On the cardinality of Hausdorff spaces.
On the cardinality of Hausdorff spaces
The aim of this paper is to show, using the reflection principle, three new cardinal inequalities. These results improve some well-known bounds on the cardinality of Hausdorff spaces.