Addition theorems and $D$-spaces

Aleksander V. Arhangel'skii; Raushan Z. Buzyakova

Displaying similar documents to “Addition theorems and $D$ -spaces”

On spaces with point-countable $k$ -systems

Iwao Yoshioka (2004)

Commentationes Mathematicae Universitatis Carolinae

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This paper deals with the behavior of $M$ -spaces, countably bi-quasi- $k$ -spaces and singly bi-quasi- $k$ -spaces with point-countable $k$ -systems. For example, we show that every $M$ -space with a point-countable $k$ -system is locally compact paracompact, and every separable singly bi-quasi- $k$ -space with a point-countable $k$ -system has a countable $k$ -system. Also, we consider equivalent relations among spaces entried in Table 1 in Michael’s paper [15] when the spaces have point-countable $k$ -systems. ...

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 $\leq 2^{ω}$ , 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....

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...

Displaying similar documents to “Addition theorems and D -spaces”

On spaces with point-countable k -systems

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

Remainders of metrizable and close to metrizable spaces

Displaying similar documents to “Addition theorems and $D$ -spaces”

On spaces with point-countable $k$ -systems

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