Abstract
The main results of this paper are that
(1) a space X is g-developable if and only if it is a weak-open π 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.
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References
P. S. Aleksandrov: On some results concerning topological spaces and thier continuous mappings. Proc. Symp. Gen. Top. (Prague, 1961). 1962, pp. 41–54.
P. S. Alekandrov, V. Niemytzki: The condition of metrizability of topological spaces and the axiom of symmetry. Rec. Math. Moscow 3 (1938), 663–672. (In Russian.)
P. S. Alexandrov: On the metrisation of topological spaces. Bull. Acad. Pol. Math., Astron., Phys. 8 (1960), 135–140. (In Russian.)
A. J. Arkhangels’kij: On mappings of metric spaces. Sov. Math. Dokl. 3 (1962), 953–956.
A. J. Arkhangel’skij: Mapping and spaces. Russ. Math. Surv. 21 (1966), 115–162.
L. Foged: On g-metrizability. Pac. J. Math. 98 (1982), 327–332.
S. P. Franklin: Spaces in which sequences suffice. Fundam. Math. 57 (1965), 107–115.
J. A. Guthrie: A characterization of ℵ0. Gen. Topology Appl. 1 (1971), 105–110.
R. W. Heath: On open mappings and certain spaces satisfying the first countability axiom. Fundam. Math. 57 (1965), 91–96.
Y. Ikeda, C. Liu, and Y. Tanaka: Quotient compact images of metric spaces, and related matters. Topology Appl. 122 (2002), 237–252.
K. B. Lee: On certain g-first countable spaces. Pac. J. Math. 65 (1976), 113–118.
J. Li: A note on g-metrizable spaces. Czechoslovak Math. J. 53 (2003), 491–495.
Z. Li, S. Lin: On the weak-open images of metric spaces. Czechoslovak Math. J. 54 (2004), 393–400.
S. Lin: On sequence-covering s-mappings. Adv. Math. Beijing 25 (1996), 548–551. (In Chinese.)
S. Lin: Generalized Metric Spaces and Mappings. China Science Press, Beijing, 1995. (In Chinese.)
S. Lin, P. Yan: Notes on cfp-covers. Commentat. Math. Univ. Carolinae 44 (2003), 295–306.
S. Lin, P. Yan: On sequence-covering compact mappings. Acta Math. Sin. 44 (2001), 175–182.
F. Siwiec: On defining a space by a weak base. Pac. J. Math. 52 (1974), 233–245.
F. Siwiec: Sequence-covering and countably bi-quotient mappings. General Topology Appl. 1 (1971), 143–154.
Y. Tanaka: Symmetric spaces, g-developable spaces and g-metrizable spaces. Math. Jap. 36 (1991), 71–84.
S. Xia: Characterizations of certain g-first countable spaces. Adv. Math. Beijing 29 (2000), 61–64. (In Chinese.)
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Xia, S. Weak-open compact images of metric spaces. Czech Math J 58, 447–455 (2008). https://doi.org/10.1007/s10587-008-0026-7
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DOI: https://doi.org/10.1007/s10587-008-0026-7