Geodesic
$\aleph_0$-spaces and images of separable metric spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 62-67.

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

A space $X$ is an $\aleph_0$-space if and only if $X$ is a sequencecovering and compact-covering image of a separable metric space. It follows that a space $X$ is a $k$-and-$\aleph_0$-space if and only if $X$ is a sequencecovering and compact-covering, quotient image of a separable metric space. 
@article{SEMR_2005_2_a3,
     author = {Y. Ge},
     title = {$\aleph_0$-spaces and images of separable metric spaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {62--67},
     publisher = {mathdoc},
     volume = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2005_2_a3/}
}
TY  - JOUR
AU  - Y. Ge
TI  - $\aleph_0$-spaces and images of separable metric spaces
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2005
SP  - 62
EP  - 67
VL  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2005_2_a3/
LA  - en
ID  - SEMR_2005_2_a3
ER  - 
%0 Journal Article
%A Y. Ge
%T $\aleph_0$-spaces and images of separable metric spaces
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2005
%P 62-67
%V 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2005_2_a3/
%G en
%F SEMR_2005_2_a3
Y. Ge. $\aleph_0$-spaces and images of separable metric spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 62-67. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a3/

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

[2] Y. Ikeda, C. Liu, Y. Tanaka, “Quotient compact images of metric spaces, and related matters”, Topology Appl., 122 (2002), 237–252 | DOI | MR | Zbl

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

[4] G. Gruenhage, “Generalized metric spaces”, Handbook of Set-Theoretic Topology, eds. K. Kunen and J. E. Vaughan, North-Holland, Amsterdan, 1984, 423–501 | MR

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

[6] S. Lin, Generalized metric spaces and mappings, Chinese Science Press, Beijing, 1995 (Chinese) | MR

[7] S. Lin, Point-countable covers and sequence-covering mappings, Chinese Science Press, Beijing, 2002 (Chinese) | MR

[8] S. Lin, metric spaces and topologies on function spaces, Chinese Science Press, Beijing, 2004 (Chinese) | MR

[9] S. Lin, C. Liu, M. Dai, “Images on locally separable metric spaces”, Acta. Math. Sinica, 13 (1997), 1–8 | MR

[10] S. Lin, P. Yan, “Sequence-Covering Maps of Metric Spaces”, Top. Appl., 109 (2001), 301–314 | DOI | MR | Zbl

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

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

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

[14] F. Siwiec, “Sequence-covering and countably bi-quotient mappings”, General Topology Appl., 1 (1971), 143–154 | DOI | MR | Zbl

[15] Y. Tanaka, “$\sigma$-hereditarily closure-preserving $k$-networks and $g$-metrizability”, Proc. Amer. Math. Soc., 112 (1991), 283–290 | MR | Zbl

[16] Y. Tanaka, “Theory of $k$-networks”, Questions Answers in Gen. Topology, 12 (1994), 139–164 | MR | Zbl

[17] Y. Tanaka, “Theory of $k$-networks II”, Questions Answers in Gen. Topology, 19 (2001), 27–46 | MR | Zbl

[18] P. Yan, S. Lin, S. Jiag, “Metrizability is preserved by closed and sequence-covering maps”, 2000 Summer Conference on Topology and its Appl., June 26–29, Maimi University, Oxford, Ohio, USA