Weak-open compact images of metric spaces
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 447-455 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The main results of this paper are that (1) a space $X$ is $g$-developable if and only if it is a weak-open $\pi $ image of a metric space, one consequence of the result being the correction of an error in the paper of Z. Li and S. Lin; (2) characterizations of weak-open compact images of metric spaces, which is another answer to a question in in the paper of Y. Ikeda, C. liu and Y. Tanaka.
The main results of this paper are that (1) a space $X$ is $g$-developable if and only if it is a weak-open $\pi $ image of a metric space, one consequence of the result being the correction of an error in the paper of Z. Li and S. Lin; (2) characterizations of weak-open compact images of metric spaces, which is another answer to a question in in the paper of Y. Ikeda, C. liu and Y. Tanaka.
Classification : 54D55, 54E15, 54E40, 54E99
Keywords: $g$-developable; $\pi $-mapping; weak-open mapping; CWC-map; uniform weak base
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Xia, Shengxiang. Weak-open compact images of metric spaces. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 2, pp. 447-455. http://geodesic.mathdoc.fr/item/CMJ_2008_58_2_a9/

[1] P. S.  Aleksandrov: On some results concerning topological spaces and thier continuous mappings. Proc. Symp. Gen. Top. (Prague, 1961), 1962, pp. 41–54. | MR

[2] P. S.  Alekandrov, V.  Niemytzki: The condition of metrizability of topological spaces and the axiom of symmetry. Rec. Math. Moscow 3 (1938), 663–672. (Russian)

[3] P. S.  Alexandrov: On the metrisation of topological spaces. Bull. Acad. Pol. Math., Astron., Phys. 8 (1960), 135–140. (Russian) | MR

[4] A. J.  Arkhangels’kij: On mappings of metric spaces. Sov. Math. Dokl. 3 (1962), 953–956.

[5] A. J.  Arkhangel’skij: Mapping and spaces. Russ. Math. Surv. 21 (1966), 115–162. | DOI

[6] L.  Foged: On $g$-metrizability. Pac. J.  Math. 98 (1982), 327–332. | MR | Zbl

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

[8] J. A. Guthrie: A characterization of $\aleph _{0}$-spaces. Gen. Topology Appl. 1 (1971), 105–110. | DOI | MR

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

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

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

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

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

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

[15] S.  Lin: Generalized Metric Spaces and Mappings. China Science Press, Beijing, 1995. (Chinese) | MR

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

[17] S.  Lin, P.  Yan: On sequence-covering compact mappings. Acta Math. Sin. 44 (2001), 175–182. | MR

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

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

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

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