Displaying similar documents to “On spaces with point-countable k -systems”

Addition theorems and D -spaces

Aleksander V. Arhangel'skii, Raushan Z. Buzyakova (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is proved that if a regular space X is the union of a finite family of metrizable subspaces then X is a D -space in the sense of E. van Douwen. It follows that if a regular space X of countable extent is the union of a finite collection of metrizable subspaces then X is Lindelöf. The proofs are based on a principal result of this paper: every space with a point-countable base is a D -space. Some other new results on the properties of spaces which are unions of a finite collection of...

Remainders of metrizable and close to metrizable spaces

A. V. Arhangel'skii (2013)

Fundamenta Mathematicae

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We continue the study of remainders of metrizable spaces, expanding and applying results obtained in [Fund. Math. 215 (2011)]. Some new facts are established. In particular, the closure of any countable subset in the remainder of a metrizable space is a Lindelöf p-space. Hence, if a remainder of a metrizable space is separable, then this remainder is a Lindelöf p-space. If the density of a remainder Y of a metrizable space does not exceed 2 ω , then Y is a Lindelöf Σ-space. We also show...

A note on topological groups and their remainders

Liang-Xue Peng, Yu-Feng He (2012)

Czechoslovak Mathematical Journal

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In this note we first give a summary that on property of a remainder of a non-locally compact topological group G in a compactification b G makes the remainder and the topological group G all separable and metrizable. If a non-locally compact topological group G has a compactification b G such that the remainder b G ∖ G of G belongs to 𝒫 , then G and b G ∖ G are separable and metrizable, where 𝒫 is a class of spaces which satisfies the following conditions: (1) if X ∈ 𝒫 , then every compact subset of the...

A generalization of Čech-complete spaces and Lindelöf Σ -spaces

Aleksander V. Arhangel'skii (2013)

Commentationes Mathematicae Universitatis Carolinae

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The class of s -spaces is studied in detail. It includes, in particular, all Čech-complete spaces, Lindelöf p -spaces, metrizable spaces with the weight ≤ 2 ω , but countable non-metrizable spaces and some metrizable spaces are not in it. It is shown that s -spaces are in a duality with Lindelöf Σ -spaces: X is an s -space if and only if some (every) remainder of X in a compactification is a Lindelöf Σ -space [Arhangel’skii A.V., Remainders of metrizable and close to metrizable spaces, Fund. Math....