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A very general covering property

Paolo Lipparini (2012)

Commentationes Mathematicae Universitatis Carolinae

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 β -normal Tychonoff space which is not normal

Eva Murtinová (2002)

Commentationes Mathematicae Universitatis Carolinae

α -normality and β -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 β -normal non-normal space and an example of a Hausdorff α -normal non-regular space.

AB-compacta

Isaac Gorelic, István Juhász (2008)

Commentationes Mathematicae Universitatis Carolinae

About remainders in compactifications of homogeneous spaces

D. Basile, Angelo Bella (2009)

Commentationes Mathematicae Universitatis Carolinae

We prove a dichotomy theorem for remainders in compactifications of homogeneous spaces: given a homogeneous space X , every remainder of X 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 w c s -covers and w c s * -networks on the Vietoris hyperspace ( X )

Luong Quoc Tuyen, Ong V. Tuyen, Phan D. Tuan, Nguzen X. Truc (2023)

Commentationes Mathematicae Universitatis Carolinae

We study some generalized metric properties on the hyperspace ( X ) of finite subsets of a space X endowed with the Vietoris topology. We prove that X has a point-star network consisting of (countable) w c s -covers if and only if so does ( X ) . Moreover, X has a sequence of w c s -covers with property ( P ) which is a point-star network if and only if so does ( X ) , where ( P ) 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

Yan-Kui Song (1999)

Commentationes Mathematicae Universitatis Carolinae

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)].

Absolutely strongly star-Hurewicz spaces

Yan-Kui Song (2015)

Open Mathematics

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.

Currently displaying 201 – 220 of 1977