Spaces with a~locally countable $sn$-network
Lobachevskii journal of mathematics, Tome 26 (2007), pp. 33-49.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we discuss a class of spaces with a locally countable $sn$-network. We give some characterizations of this class and investigate variance and inverse invariance of this class under certain mappings.
Keywords: $sn$-network, $cs$-network, weak-base, perfectmapping, (strongly) Lindelöf mapping, finite subsequence-covering mapping.
@article{LJM_2007_26_a4,
     author = {X. Ge},
     title = {Spaces with a~locally countable $sn$-network},
     journal = {Lobachevskii journal of mathematics},
     pages = {33--49},
     publisher = {mathdoc},
     volume = {26},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2007_26_a4/}
}
TY  - JOUR
AU  - X. Ge
TI  - Spaces with a~locally countable $sn$-network
JO  - Lobachevskii journal of mathematics
PY  - 2007
SP  - 33
EP  - 49
VL  - 26
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2007_26_a4/
LA  - en
ID  - LJM_2007_26_a4
ER  - 
%0 Journal Article
%A X. Ge
%T Spaces with a~locally countable $sn$-network
%J Lobachevskii journal of mathematics
%D 2007
%P 33-49
%V 26
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2007_26_a4/
%G en
%F LJM_2007_26_a4
X. Ge. Spaces with a~locally countable $sn$-network. Lobachevskii journal of mathematics, Tome 26 (2007), pp. 33-49. http://geodesic.mathdoc.fr/item/LJM_2007_26_a4/

[1] A. V. Arhangel'skii, “Mappings and spaces”, Russian Math. Surveys, 21 (1966), 115–162 | DOI | MR

[2] A. Arhangel'skii and S. Franklin, “Ordinal invariants for topological spaces”, Michigan Math. J., 15 (1968), 313–320 | DOI | MR

[3] B. Blacar and P. Simon, “Disjoint refinement”, Handbook of Boolean Algebras, V. 2, North-Holland, Amsterdam, 332–386

[4] J. R. Boone and F. Siwiec, “Sequentially quotient mappings”, Czech. Math. J., 26 (1976), 174–182 | MR | Zbl

[5] J. Chaber, “Conditions which imply compactness in countably compact spaces”, Bull. Pol. Acad. Math., 24 (1976), 993–998 | MR

[6] S. W. Davis, “More on Cauchy condition”, Topology Proc., 9 (1984), 31–36 | MR | Zbl

[7] R. Engelking, General Topology, revised and completed edition, Heldermann, Berlin, 1989 | MR | Zbl

[8] S. P. Franklin, “Spaces in which sequence suffice”, Fund. Math., 57 (1965), 107–115 | MR | Zbl

[9] D. Gale, “Compact sets of functions and function rings”, Proc. Amer. Math. Soc., 1 (1950), 303–308 | DOI | MR | Zbl

[10] Z. Gao, “$\aleph$-space is invariant under perfect mappings”, Q and A in General Topology, 5 (1987), 271–279 | MR | Zbl

[11] Y. Ge, “On $sn$-metrizable spaces”, Acta Math. Sinica, 45 (2002), 355–360 | MR | Zbl

[12] Y. Ge, “Characterizations of $sn$-metrizable spaces”, Publ. Inst. Math., Nouv. Ser., 74:88 (2003), 121–128 | MR

[13] Y. Ge, “Spaces with countable $sn$-networks”, Comment Math. Univ. Carolinae, 45 (2004), 169–176 | MR | Zbl

[14] G. Gruenhage, E. Michael and Y. Tanaka, “Spaces determined by point-countable covers”, Pacific J. Math., 113 (1984), 303–332 | MR | Zbl

[15] J. A. Guthrie, “A characterization of $\aleph_0$-spaces”, General Topology Appl., 1 (1971), 105–110 | DOI | MR | Zbl

[16] S. Lin, “On normal separable $\aleph$-space”, Q and A in General Topology, 5 (1987), 249–254 | MR | Zbl

[17] S. Lin, “Spaces with a locally countable k-network”, Northeastern Math. J., 6 (1990), 39–44 | MR | Zbl

[18] S. Lin, “On $g$-metrizable spaces”, Chinese Ann. Math., Ser A, 13 (1992), 403–409 | MR | Zbl

[19] S. Lin, Generalized Metric Spaces and Mappings, Chinese Science Press, Beijing, 1995 | MR

[20] S. Lin, “A note on the Arens' spaces and sequential fan”, Topology Appl., 81 (1997), 185–196 | DOI | MR | Zbl

[21] S. Lin, “A note on spaces with a locally countable k-network”, J. of Jishou Univ., 18:3 (1997), 10–12 | MR

[22] S. Lin, Point-Countable Covers and Sequence-Covering Mappings, Chinese Science Press, Beijing, 2002 | MR

[23] S. Lin and P. Yan,, “Sequence-covering maps of metric spaces”, Topology. Appl., 109 (2001), 301–314 | DOI | MR | Zbl

[24] C. Liu and M. Dai, “Spaces with a locally countable weak base”, Math. Japonica, 41 (1995), 261–267 | MR | Zbl

[25] C. Liu, “Notes on weak bases”, Q and A in General Topology, 22 (2004), 39–42 | MR | Zbl

[26] E. A. Michael, “$\aleph_0$-spaces”, J. Math. Mech., 15 (1966), 983–1002 | MR | Zbl

[27] P. O'Meara, “On paracompactness in function spaces with the compact-open topology”, Proc. Amer. Math. Soc., 29 (1971), 183–189 | DOI | MR

[28] J. Roitman, “Basic $S$ and $L$”, Handbook of Set-Theoretic Topology, eds. Kumen K. and Vaughan J. E., North-Holland, Amsterdan, 295–326 | MR | Zbl

[29] F. Siwiec, “On defining a space by a werk base”, Pacific J. Math., 52 (1974), 233–245 | MR | Zbl

[30] Y. Tanaka, “Point-countable covers and $k$-networks”, Topology Proc., 12 (1987), 327–349 | MR | Zbl

[31] Y. Tanaka, “Theory of $k$-networks II”, Q and A in General Topology, 19 (2001), 27–46 | MR | Zbl

[32] Y. Tanaka and Y. Ge, “Around quotient compact images of metric spaces, and symmetric spaces”, Houston J. Math., 32 (2006), 99–117 | MR | Zbl

[33] Y. Tanaka and Z. Li, “Certain covering-maps and $k$-networks, and related matters”, Topology Proc., 27 (2003), 317–334 | MR | Zbl