Geodesic
On weak-open $\pi$-images of metric spaces
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 1011-1018
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper, we give some characterizations of metric spaces under weak-open $\pi$-mappings, which prove that a space is $g$-developable (or Cauchy) if and only if it is a weak-open $\pi$-image of a metric space.
In this paper, we give some characterizations of metric spaces under weak-open $\pi$-mappings, which prove that a space is $g$-developable (or Cauchy) if and only if it is a weak-open $\pi$-image of a metric space.
Classification : 54C10, 54D55, 54E40, 54E99
Keywords: weak-open mappings; $\pi$-mappings; $g$-developable spaces; Cauchy spaces; cs-covers; sn-covers; weak-developments; point-star networks 
@article{CMJ_2006_56_3_a19,
     author = {Li, Zhaowen},
     title = {On weak-open $\pi$-images of metric spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1011--1018},
     year = {2006},
     volume = {56},
     number = {3},
     mrnumber = {2261673},
     zbl = {1164.54365},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a19/}
}
TY  - JOUR
AU  - Li, Zhaowen
TI  - On weak-open $\pi$-images of metric spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2006
SP  - 1011
EP  - 1018
VL  - 56
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a19/
LA  - en
ID  - CMJ_2006_56_3_a19
ER  - 
%0 Journal Article
%A Li, Zhaowen
%T On weak-open $\pi$-images of metric spaces
%J Czechoslovak Mathematical Journal
%D 2006
%P 1011-1018
%V 56
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a19/
%G en
%F CMJ_2006_56_3_a19
Li, Zhaowen. On weak-open $\pi$-images of metric spaces. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 1011-1018. http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a19/

[1] A. V.  Arhangel’skii: Mappings and spaces. Russian Math. Surveys 21 (1996), 115–162. | DOI | MR

[2] V. I.  Ponomarev: Axioms of countability of continuous mappings. Bull. Pol. Acad. Math. 8 (1960), 127–133. | MR

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

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

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

[6] P. S.  Alexandroff, V.  Niemytzki: The condition of metrizability of topological spaces and the axiom of symmetry. Mat. Sb. 3 (1938), 663–672.

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

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

[9] S.  Lin: Generalized Metric Spaces and Mappings. Chinese Scientific Publ., Beijing, 1995.

[10] S.  Lin: On sequence-covering $s$-mappings. Adv. Math. 25 (1996), 548–551. | MR | Zbl

[11] S.  Lin, Y.  Zhou, and P.  Yan: On sequence-covering $\pi $-mappings. Acta Math. Sinica 45 (2002), 1157–1164. | MR

[12] R. W.  Heath: On open mappings and certain spaces satisfying the first countability axiom. Fund. Math. 57 (1965), 91–96. | DOI | MR | Zbl

[13] J. A.  Kofner: On a new class of spaces and some problems of symmetrizability theory. Soviet Math. Dokl. 10 (1969), 845–848. | Zbl

[14] D. K.  Burke: Cauchy sequences in semimetric spaces. Proc. Amer. Math. Soc. 33 (1972), 161–164. | DOI | MR | Zbl

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

[16] G.  Gruenhage: Generalized metric spaces. In: Handbook of Set-theoretic Topology, K. Kunen, J. E. Vaughan (eds.), North-Holland, Amsterdam, 1984, pp. 423–501. | MR | Zbl

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

[18] Z.  Li: On the weak-open images of metric spaces. Czechoslovak Math.  J. 54 (2004), 393–400. | DOI | MR | Zbl