On zero-dimensionality of subgroups of locally compact groups
Improving the recent result of the author we show that is equivalent to for every subgroup of a Hausdorff locally compact group .
On -continuous functions
On -continuous functions
Classes of functions continuous in various senses, in particular -continuous, -continuous, feeblz continuous a.o., and relations between the classes, are studied.
On -distance in three dimensional space.
On -embedded sets and extension of mappings
We introduce and study -embedded sets and apply them to generalize the Kuratowski Extension Theorem.
On -level topological groups.
On -normal and -normal spaces
We define two natural normality type properties, -normality and -normality, and compare these notions to normality. A natural weakening of Jones Lemma immediately leads to generalizations of some important results on normal spaces. We observe that every -normal, pseudocompact space is countably compact, and show that if is a dense subspace of a product of metrizable spaces, then is normal if and only if is -normal. All hereditarily separable spaces are -normal. A space is normal if and...
On --open sets and a decomposition of almost--continuity.
On β-favorability of the strong Choquet game
In the main result, partially answering a question of Telgársky, the following is proven: if X is a first countable R₀-space, then player β (i.e. the EMPTY player) has a winning strategy in the strong Choquet game on X if and only if X contains a nonempty -subspace which is of the first category in itself.
On -continuous selections of small multifunctions and covering properties
The spaces for which each -continuous function can be extended to a -small point-open l.s.cṁultifunction (resp. point-closed u.s.cṁultifunction) are studied. Some sufficient conditions and counterexamples are given.
On -sets and associated weak separation axioms.
On Δ-spaces and fundamental dimension in the sense of Borsuk
On --open sets.
On -closed sets and some forms of continuity
In this paper, we further the study of -compactness a generalization of quasi-H-closed sets and its applications to some forms of continuity using -open and -open sets. Among other results, it is shown a weakly -retract of a Hausdorff space is a -closed subset of .
On -continuity and strong -continuity.
On -generalized closed sets.
On -precontinuous functions.
On -regular spaces.
On κ-Lindelöf spaces
We use the Hausdorff pseudocharacter to bound the cardinality and the Lindelöf degree of κ-Lindelöf Hausdorff spaces.
On -caliber and an application of Prikry’s partial order
We study the concept of -caliber as an alternative to the well known concept of caliber. -caliber and caliber values coincide for regular cardinals greater than or equal to the Souslin number of a space. Unlike caliber, -caliber may take on values below the Souslin number of a space. Under Martin’s axiom, is a -caliber of . Prikry’s poset is used to settle a problem by Fedeli regarding possible values of very weak caliber.