-Ponomarev’s System and Images of Locally Separable Metric Spaces
Tran Van An, Luong Quoc Tuyen (2013)
Publications de l'Institut Mathématique
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Tran Van An, Luong Quoc Tuyen (2013)
Publications de l'Institut Mathématique
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Luong Quoc Tuyen (2013)
Publications de l'Institut Mathématique
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Shu Hao Sun (1988)
Commentationes Mathematicae Universitatis Carolinae
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Alexander Shibakov (1995)
Commentationes Mathematicae Universitatis Carolinae
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We prove some closed mapping theorems on -spaces with point-countable -networks. One of them generalizes Lašnev’s theorem. We also construct an example of a Hausdorff space with a countable base that admits a closed map onto metric space which is not compact-covering. Another our result says that a -space with a point-countable -network admitting a closed surjection which is not compact-covering contains a closed copy of .
Zhaowen Li (2006)
Archivum Mathematicum
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In this paper, spaces with -locally countable weak-bases are characterized as the weakly open msss-images of metric spaces (or -first countable spaces with -locally countable -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, -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...