Geodesic
$g$-metrizable spaces and the images of semi-metric spaces
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1141-1149 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper, we prove that a space $X$ is a $g$-metrizable space if and only if $X$ is a weak-open, $\pi $ and $\sigma $-image of a semi-metric space, if and only if $X$ is a strong sequence-covering, quotient, $\pi $ and $mssc$-image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.
In this paper, we prove that a space $X$ is a $g$-metrizable space if and only if $X$ is a weak-open, $\pi $ and $\sigma $-image of a semi-metric space, if and only if $X$ is a strong sequence-covering, quotient, $\pi $ and $mssc$-image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.
Classification : 54C10, 54D55, 54E25, 54E35, 54E40
Keywords: $g$-metrizable spaces; $sn$-metrizable spaces; weak-open mappings; strong sequence-covering mappings; quotient mappings; $\pi $-mappings; $\sigma $-mappings; $mssc$-mappings 
@article{CMJ_2007_57_4_a4,
     author = {Ge, Ying and Lin, Shou},
     title = {$g$-metrizable spaces and the images of semi-metric spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1141--1149},
     year = {2007},
     volume = {57},
     number = {4},
     mrnumber = {2357584},
     zbl = {1174.54018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a4/}
}
TY  - JOUR
AU  - Ge, Ying
AU  - Lin, Shou
TI  - $g$-metrizable spaces and the images of semi-metric spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2007
SP  - 1141
EP  - 1149
VL  - 57
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a4/
LA  - en
ID  - CMJ_2007_57_4_a4
ER  - 
%0 Journal Article
%A Ge, Ying
%A Lin, Shou
%T $g$-metrizable spaces and the images of semi-metric spaces
%J Czechoslovak Mathematical Journal
%D 2007
%P 1141-1149
%V 57
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a4/
%G en
%F CMJ_2007_57_4_a4
Ge, Ying; Lin, Shou. $g$-metrizable spaces and the images of semi-metric spaces. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 4, pp. 1141-1149. http://geodesic.mathdoc.fr/item/CMJ_2007_57_4_a4/

[1] A. V. Arhangel’skiǐ: Mappings and spaces. Russian Math. Surveys 21 (1966), 115–162. | MR

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

[3] R. Engelking: General Topology (revised and completed edition). Heldermann-Verlag, Berlin, 1989. | MR

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

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

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

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

[8] J. Li: A note on $g$-metrizable spaces. Czech. Math. J. 53 (2003), 491–495. | DOI | MR | Zbl

[9] Z. Li: A note on $\aleph $-spaces and $g$-metrizable spaces. Czech. Math. J. 55 (2005), 803–808. | DOI | MR | Zbl

[10] Z. Li and S. Lin: On the weak-open images of metric spaces. Czech. Math. J. 54 (2004), 393–400. | DOI | MR

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

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

[13] S. Lin and P. Yan: Notes on $cfp$-covers. Comment. Math. Univ. Carolinae 44 (2003), 295–306. | MR

[14] J. Nagata: Generalized metric spaces I. Topics in General Topology, North-Holland, Amsterdam, 1989, pp. 313–366. | MR | Zbl

[15] V. I. Ponomarev: Axioms of countability and continuous mappings. Bull Pol. Acad Math. 8 (1960), 127–134. | MR

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

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

[18] Y. Tanaka: Symmetric spaces, $g$-developable spaces and $g$-metrizable spaces. Math. Japonica 36 (1991), 71–84. | MR | Zbl

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

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