On a construction of perfectly normal spaces and its applications to dimension theory
On a dense -diagonal.
On a Question of Ljubiša Kočinac
On a theorem of Jones and Heath concerning separable normal spaces
On almost and weak forms of continuity of functions and multifunctions
On bitopological local compactness
On butterfly-points in , Tychonoff products and weak Lindelöf numbers
Let be the Tychonoff product of -many Tychonoff non-single point spaces . Let be a point in the closure of some whose weak Lindelöf number is strictly less than the cofinality of . Then we show that is not normal. Under some additional assumptions, is a butterfly-point in . In particular, this is true if either or and is infinite and not countably cofinal.
On collectionwise normality
On completely regular spaces
On continuous images of almost Tychonoff cubes
On dense subspaces satisfying stronger separation axioms
We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of -weight less than has a dense completely Hausdorff (and hence Urysohn) subspace. We show that...
On -compactifications and -compactifiable spaces.
On expansions of a Urysohn space to a regular space.
On generalizations of regular-Lindelöf spaces.
On Hausdorff compactifications of non-locally compact spaces.
On hereditarily normal topological groups
We investigate hereditarily normal topological groups and their subspaces. We prove that every compact subspace of a hereditarily normal topological group is metrizable. To prove this statement we first show that a hereditarily normal topological group with a non-trivial convergent sequence has -diagonal. This implies, in particular, that every countably compact subspace of a hereditarily normal topological group with a non-trivial convergent sequence is metrizable. Another corollary is that under...
On hereditarily separable Hausdorff spaces in the constructible universe
On hereditary normality of , Kunen points and character
We show that is not normal, if is a limit point of some countable subset of , consisting of points of character . Moreover, such a point is a Kunen point and a super Kunen point.
On locally finite coverings
On Nearly Paracompact Spaces