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
On Nearly Paracompact Spaces and Nearly Full Normality
On non-normality points, Tychonoff products and Suslin number
Let a space be Tychonoff product of -many Tychonoff nonsingle point spaces . Let Suslin number of be strictly less than the cofinality of . Then we show that every point of remainder is a non-normality point of its Čech–Stone compactification . In particular, this is true if is either or and a cardinal is infinite and not countably cofinal.
On normal lattices and Wallman spaces.
On normality and countable paracompactness
On Pervin's example concerning the connected-open topology.
On Preservation Of Normality.
On relatively almost countably compact subsets
A subset of a space is almost countably compact in if for every countable cover of by open subsets of , there exists a finite subfamily of such that . In this paper we investigate the relationship between almost countably compact spaces and relatively almost countably compact subsets, and also study various properties of relatively almost countably compact subsets.
On relatively almost Lindelöf subsets
A subspace of a space is almost Lindelöf (strongly almost Lindelöf) in if for every open cover of (of by open subsets of ), there exists a countable subset of such that . In this paper we investigate the relationships between relatively almost Lindelöf subset and relatively strongly almost Lindelöf subset by giving some examples, and also study various properties of relatively almost Lindelöf subsets and relatively strongly almost Lindelöf subsets.
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 the combinatorial principle P(c)
On the concept of E-regularity for fuzzy topology