Previous |  Up |  Next

Article

Title: Weak-open compact images of metric spaces (English)
Author: Xia, Shengxiang
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 2
Year: 2008
Pages: 447-455
Summary lang: English
.
Category: math
.
Summary: 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. (English)
Keyword: $g$-developable
Keyword: $\pi $-mapping
Keyword: weak-open mapping
Keyword: CWC-map
Keyword: uniform weak base
MSC: 54D55
MSC: 54E15
MSC: 54E40
MSC: 54E99
idZBL: Zbl 1174.54021
idMR: MR2411100
.
Date available: 2009-09-24T11:55:54Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/128268
.
Reference: [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 0145472
Reference: [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)
Reference: [3] P. S.  Alexandrov: On the metrisation of topological spaces.Bull. Acad. Pol. Math., Astron., Phys. 8 (1960), 135–140. (Russian) MR 0114199
Reference: [4] A. J.  Arkhangels’kij: On mappings of metric spaces.Sov. Math. Dokl. 3 (1962), 953–956.
Reference: [5] A. J.  Arkhangel’skij: Mapping and spaces.Russ. Math. Surv. 21 (1966), 115–162. 10.1070/RM1966v021n04ABEH004169
Reference: [6] L.  Foged: On $g$-metrizability.Pac. J.  Math. 98 (1982), 327–332. Zbl 0478.54025, MR 0650013
Reference: [7] S. P.  Franklin: Spaces in which sequences suffice.Fundam. Math. 57 (1965), 107–115. Zbl 0132.17802, MR 0180954, 10.4064/fm-57-1-107-115
Reference: [8] J. A. Guthrie: A characterization of $\aleph _{0}$-spaces.Gen. Topology Appl. 1 (1971), 105–110. MR 0288726, 10.1016/0016-660X(71)90116-4
Reference: [9] R.  W.  Heath: On open mappings and certain spaces satisfying the first countability axiom.Fundam. Math. 57 (1965), 91–96. Zbl 0134.41802, MR 0179763, 10.4064/fm-57-1-91-96
Reference: [10] Y.  Ikeda, C.  Liu, and Y.  Tanaka: Quotient compact images of metric spaces, and related matters.Topology Appl. 122 (2002), 237–252. MR 1919303, 10.1016/S0166-8641(01)00145-6
Reference: [11] K. B.  Lee: On certain $g$-first countable spaces.Pac. J.  Math. 65 (1976), 113–118. Zbl 0359.54022, MR 0423307, 10.2140/pjm.1976.65.113
Reference: [12] J.  Li: A note on $g$-metrizable spaces.Czechoslovak Math.  J. 53 (2003), 491–495. Zbl 1026.54026, MR 1983468, 10.1023/A:1026208025139
Reference: [13] Z.  Li, S.  Lin: On the weak-open images of metric spaces.Czechoslovak Math.  J. 54 (2004), 393–400. MR 2059259, 10.1023/B:CMAJ.0000042377.80659.fb
Reference: [14] S.  Lin: On sequence-covering $s$-mappings.Adv. Math. Beijing 25 (1996), 548–551. (Chinese) Zbl 0864.54026, MR 1453163
Reference: [15] S.  Lin: Generalized Metric Spaces and Mappings.China Science Press, Beijing, 1995. (Chinese) MR 1375020
Reference: [16] S.  Lin, P.  Yan: Notes on $cfp$-covers.Commentat. Math. Univ. Carolinae 44 (2003), 295–306. MR 2026164
Reference: [17] S.  Lin, P.  Yan: On sequence-covering compact mappings.Acta Math. Sin. 44 (2001), 175–182. MR 1819992
Reference: [18] F. Siwiec: On defining a space by a weak base.Pac. J. Math. 52 (1974), 233–245. Zbl 0285.54022, MR 0350706
Reference: [19] F.  Siwiec: Sequence-covering and countably bi-quotient mappings.General Topology Appl. 1 (1971), 143–154. Zbl 0218.54016, MR 0288737, 10.1016/0016-660X(71)90120-6
Reference: [20] Y.  Tanaka: Symmetric spaces, $g$-developable spaces and $g$-metrizable spaces.Math. Jap. 36 (1991), 71–84. Zbl 0732.54023, MR 1093356
Reference: [21] S.  Xia: Characterizations of certain $g$-first countable spaces.Adv. Math. Beijing 29 (2000), 61–64. (Chinese) Zbl 0999.54010, MR 1769127
.

Files

Files Size Format View
CzechMathJ_58-2008-2_10.pdf 269.6Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo