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Displaying similar documents to “Closed mapping theorems on k -spaces with point-countable k -networks”

k -systems, k -networks and k -covers

Jinjin Li, Shou Lin (2006)

Czechoslovak Mathematical Journal

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The concepts of k -systems, k -networks and k -covers were defined by A. Arhangel’skiǐ in 1964, P. O’Meara in 1971 and R. McCoy, I. Ntantu in 1985, respectively. In this paper the relationships among k -systems, k -networks and k -covers are further discussed and are established by m k -systems. As applications, some new characterizations of quotients or closed images of locally compact metric spaces are given by means of m k -systems.

Paratopological (topological) groups with certain networks

Chuan Liu (2014)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we discuss certain networks on paratopological (or topological) groups and give positive or negative answers to the questions in [Lin2013]. We also prove that a non-locally compact, k -gentle paratopological group is metrizable if its remainder (in the Hausdorff compactification) is a Fréchet-Urysohn space with a point-countable cs*-network, which improves some theorems in [Liu C., Metrizability of paratopological ( semitopological ) groups, Topology Appl. 159 (2012), 1415–1420], [Liu...

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....