A unified theory of weak separation properties.
A universal metacompact developable -space of weight m
A variant of a theorem of Sierpiński concerning partitions of continua
A very general covering property
We introduce a general notion of covering property, of which many classical definitions are particular instances. Notions of closure under various sorts of convergence, or, more generally, under taking kinds of accumulation points, are shown to be equivalent to a covering property in the sense considered here (Corollary 3.10). Conversely, every covering property is equivalent to the existence of appropriate kinds of accumulation points for arbitrary sequences on some fixed index set (Corollary 3.5)....
A weakening of , with applications to topology
A weakly pseudocompact subspace of Banach space is weakly compact
A -normal Tychonoff space which is not normal
-normality and -normality are properties generalizing normality of topological spaces. They consist in separating dense subsets of closed disjoint sets. We construct an example of a Tychonoff -normal non-normal space and an example of a Hausdorff -normal non-regular space.
AB-compacta
About remainders in compactifications of homogeneous spaces
We prove a dichotomy theorem for remainders in compactifications of homogeneous spaces: given a homogeneous space , every remainder of is either realcompact and meager or Baire. In addition we show that two other recent dichotomy theorems for remainders of topological groups due to Arhangel’skii cannot be extended to homogeneous spaces.
About -covers and -networks on the Vietoris hyperspace
We study some generalized metric properties on the hyperspace of finite subsets of a space endowed with the Vietoris topology. We prove that has a point-star network consisting of (countable) -covers if and only if so does . Moreover, has a sequence of -covers with property which is a point-star network if and only if so does , where is one of the following properties: point-finite, point-countable, compact-finite, compact-countable, locally finite, locally countable. On the other...
Absolute countable compactness of products and topological groups
In this paper, we generalize Vaughan's and Bonanzinga's results on absolute countable compactness of product spaces and give an example of a separable, countably compact, topological group which is not absolutely countably compact. The example answers questions of Matveev [8, Question 1] and Vaughan [9, Question (1)].
Absolute points in
Absolutely strongly star-Hurewicz spaces
A space X is absolutely strongly star-Hurewicz if for each sequence (Un :n ∈ℕ/ of open covers of X and each dense subset D of X, there exists a sequence (Fn :n ∈ℕ/ of finite subsets of D such that for each x ∈X, x ∈St(Fn; Un) for all but finitely many n. In this paper, we investigate the relationships between absolutely strongly star-Hurewicz spaces and related spaces, and also study topological properties of absolutely strongly star-Hurewicz spaces.
AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology
We show that AC is equivalent to the assertion that every compact completely regular topology can be extended to a compact Tychonoff topology.
Accessibility spaces, -spaces and initial topologies
Accumulation points of nowhere dense sets
Acknowledgement concerning two papers on rational dimension
Acknowledgment to the paper: “Another proof that a chain of non-empty -closed subspaces has a non-empty intersection’
Actions, functors and the bar construction
Addition and subspace theorems for asymptotic large inductive dimension
We prove the addition and subspace theorems for asymptotic large inductive dimension. We investigate a transfinite extension of this dimension and show that it is trivial.