Characterizations of spaces with $\sigma$-locally countable $sn$-networks
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 480-486.

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

The concept of a $\sigma$-locally countable mapping is used for establishing relations between metric spaces and spaces with $\sigma$-locally countable $sn$-networks ($cs^*$-networks, weak bases).
Keywords: $cs^*$-network, $sn$-network, weak base, $\sigma$-locally countable mapping, sequence-covering mapping.
@article{SEMR_2010_7_a33,
     author = {Sh. Xia},
     title = {Characterizations of spaces with $\sigma$-locally countable $sn$-networks},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {480--486},
     publisher = {mathdoc},
     volume = {7},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2010_7_a33/}
}
TY  - JOUR
AU  - Sh. Xia
TI  - Characterizations of spaces with $\sigma$-locally countable $sn$-networks
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2010
SP  - 480
EP  - 486
VL  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2010_7_a33/
LA  - en
ID  - SEMR_2010_7_a33
ER  - 
%0 Journal Article
%A Sh. Xia
%T Characterizations of spaces with $\sigma$-locally countable $sn$-networks
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2010
%P 480-486
%V 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2010_7_a33/
%G en
%F SEMR_2010_7_a33
Sh. Xia. Characterizations of spaces with $\sigma$-locally countable $sn$-networks. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 480-486. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a33/

[1] P. Alexandroff, “On some results concerning topological spaces and their continuous mappings”, Proc. Symp. Gen. Top. (Prague, 1961), 41–54 | MR

[2] Arhangel'skii, “Mapping and spaces”, Russian Math. Survey, 21 (1966), 115–162 | DOI | MR

[3] L. Foged, “On $g$-metrizability”, Pacific J. Math., 98 (1982), 327–332 | MR | Zbl

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

[5] Z. Gao, “$\aleph$-spaces is invariant under perfect mappings”, Questions and Answers. General Topology, 5 (1987), 271–279 | MR | Zbl

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

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

[8] Y. Ge, “On pseudo-sequence coverings $\pi$-images of metric spaces”, Matematicki Vesnik, 57 (2005), 113–120 | MR | Zbl

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

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

[11] K. B. Lee, “On certain $g$-first countable spaces”, Pacific J. Math., 65 (1976), 113–118 | MR | Zbl

[12] S. Lin, “On sequence-covering $s$-mappings”, Adv. Math., 25 (1996), 548–551 (in Chinese) | MR | Zbl

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

[14] S. Lin, “The sequence-covering $s$-images of metric spaces”, Northeastern. Math. J., 9 (1993), 81–85 | MR | Zbl

[15] S. Lin, P. Yan, “Sequence-covering $s$-mappings”, Topology and Its Applications, 109 (2001), 301–314 | DOI | MR | Zbl

[16] E. Michael, “A quintuple quotient quest”, General Topology and Appl., 2 (1972), 91–138 | DOI | MR | Zbl

[17] V. I. Ponomarev, “Axioms of countability and continuous mappings”, Bull. Acad. Polon. Sci. Sér. Math. Astronom. Phys., 8 (1960), 127–134 (in Russian) | MR | Zbl

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

[19] S. Xia, “The $\sigma$-locally countable images of metric spaces”, Georgian Mathematical Journal, 16 (2009), 393–399 | MR | Zbl

[20] S. Xia, “Characterizations of certain $g$-first countable spaces”, Adv. Math., 29 (2000), 61–64 (in Chinese) | MR | Zbl

[21] S. Xia, “Spaces with $\sigma$-locally countable weak bases”, Chinese Quarterly J. Math., 16 (2001), 37–41 | MR | Zbl