Closed subsets of absolutely star-Lindelöf spaces II

Yan-Kui Song

Displaying similar documents to “Closed subsets of absolutely star-Lindelöf spaces II”

Completely regular spaces

H. L. Bentley, Eva Lowen-Colebunders (1991)

Commentationes Mathematicae Universitatis Carolinae

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We conduct an investigation of the relationships which exist between various generalizations of complete regularity in the setting of merotopic spaces, with particular attention to filter spaces such as Cauchy spaces and convergence spaces. Our primary contribution consists in the presentation of several counterexamples establishing the divergence of various such generalizations of complete regularity. We give examples of: (1) a contigual zero space which is not weakly regular and is...

Lindelöf property and the iterated continuous function spaces

G. Sokolov (1993)

Fundamenta Mathematicae

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We give an example of a compact space X whose iterated continuous function spaces $C_{p} (X)$ , $C_{p} C_{p} (X), . . .$ are Lindelöf, but X is not a Corson compactum. This solves a problem of Gul’ko (Problem 1052 in [11]). We also provide a theorem concerning the Lindelöf property in the function spaces $C_{p} (X)$ on compact scattered spaces with the $ω_{1}$ th derived set empty, improving some earlier results of Pol [12] in this direction.

Linear subspace of Rl without dense totally disconnected subsets

K. Ciesielski (1993)

Fundamenta Mathematicae

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In [1] the author showed that if there is a cardinal κ such that $2^{κ} = κ^{+}$ then there exists a completely regular space without dense 0-dimensional subspaces. This was a solution of a problem of Arkhangel’skiĭ. Recently Arkhangel’skiĭ asked the author whether one can generalize this result by constructing a completely regular space without dense totally disconnected subspaces, and whether such a space can have a structure of a linear space. The purpose of this paper is to show that indeed such...

In quest of weaker connected topologies

Mihail G. Tkachenko, Vladimir Vladimirovich Tkachuk, Vladimir Vladimirovich Uspenskij, Richard Gordon Wilson (1996)

Commentationes Mathematicae Universitatis Carolinae

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We study when a topological space has a weaker connected topology. Various sufficient and necessary conditions are given for a space to have a weaker Hausdorff or regular connected topology. It is proved that the property of a space of having a weaker Tychonoff topology is preserved by any of the free topological group functors. Examples are given for non-preservation of this property by “nice” continuous mappings. The requirement that a space have a weaker Tychonoff connected topology...