On -metrizable spaces
Xun Ge (2009)
Matematički Vesnik
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Displaying similar documents to “Spaces with -weakly hereditarily closure-preserving sn-networks.”
On -metrizable spaces
Spaces with a locally countable -network.
Ge, Ying (2007)
Bulletin of TICMI
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On some generalizations of LC-spaces.
Dontchev, J., Ganster, M., Kanibir, A. (1999)
Acta Mathematica Universitatis Comenianae. New Series
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On weakly monotonically monolithic spaces
Liang-Xue Peng (2010)
Commentationes Mathematicae Universitatis Carolinae
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In this note, we introduce the concept of weakly monotonically monolithic spaces, and show that every weakly monotonically monolithic space is a -space. Thus most known conclusions on -spaces can be obtained by this conclusion. As a corollary, we have that if a regular space is sequential and has a point-countable -network then is a -space.
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 , 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 on compact scattered spaces with the th derived set empty, improving some earlier results of Pol [12] in this direction.
A note on weakly hereditarily closure-preserving families.
Shen, Jianhua, Ge, Ying, Ge, Zhihong (2006)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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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, -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...
Vietoris topology on spaces dominated by second countable ones
Carlos Islas, Daniel Jardon (2015)
Open Mathematics
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For a given space X let C(X) be the family of all compact subsets of X. A space X is dominated by a space M if X has an M-ordered compact cover, this means that there exists a family F = FK : K ∈ C(M) ⊂ C(X) such that ∪ F = X and K ⊂ L implies that FK ⊂ FL for any K;L ∈ C(M). A space X is strongly dominated by a space M if there exists an M-ordered compact cover F such that for any compact K ⊂ X there is F ∈ F such that K ⊂ F . Let K(X) D C(X){Øbe the set of all nonempty compact subsets...