Previous |  Up |  Next


Title: Closed mapping theorems on $k$-spaces with point-countable $k$-networks (English)
Author: Shibakov, A.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 36
Issue: 1
Year: 1995
Pages: 77-87
Category: math
Summary: We prove some closed mapping theorems on $k$-spaces with point-countable $k$-networks. One of them generalizes La\v snev's theorem. We also construct an example of a Hausdorff space $Ur$ with a countable base that admits a closed map onto metric space which is not compact-covering. Another our result says that a $k$-space $X$ with a point-countable $k$-network admitting a closed surjection which is not compact-covering contains a closed copy of $Ur$. (English)
Keyword: $k$-space
Keyword: $k$-network
Keyword: closed map
Keyword: compact-covering map
MSC: 54A20
MSC: 54B10
MSC: 54C10
idZBL: Zbl 0832.54011
idMR: MR1334416
Date available: 2009-01-08T18:16:10Z
Last updated: 2012-04-30
Stable URL:
Reference: [A] Arkhagel'skii A.: Factor mappings of metric spaces (in Russian).Dokl. Akad. Nauk SSSR 155 (1964), 247-250. MR 0163284
Reference: [GMT] Gruenhage G., Michael E., Tanaka Y.: Spaces determined by point-countable covers.Pacif. J. Math. 113 (1984), 303-332. Zbl 0561.54016, MR 0749538
Reference: [H] Hoshina T.: On the quotient $s$-images of metric spaces.Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 10 (1970), 265-268. Zbl 0214.49503, MR 0275358
Reference: [L] Lašnev N.: Continuous decompositions and closed mappings of metric spaces.Sov. Math. Dokl. 6 (1965), 1504-1506. MR 0192478
Reference: [M] Michael E.: $\aleph_0$-spaces.J. Math. Mech. 15 (1966), 983-1002. MR 0206907
Reference: [Miš] Miščenko A.: Spaces with pointwise denumerable basis (in Russian).Dokl. Akad. Nauk SSSR 145 (1962), 985-988 Soviet Math. Dokl. 3 (1962), 855-858. MR 0138090
Reference: [T] Tanaka Y.: Point-countable covers and $k$-networks.Topology Proceedings 12 (1987), 327-349. Zbl 0676.54035, MR 0991759
Reference: [V1] Velichko N.: Ultrasequential spaces (in Russian).Mat. Zametki 45 (1989), 15-21. MR 1002513
Reference: [V2] Velichko N.: On continuous mappings of topological spaces (in Russian).Sibirsky Mat. Zhurnal 8 (1972), 541-557. MR 0301691


Files Size Format View
CommentatMathUnivCarolRetro_36-1995-1_11.pdf 242.5Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo