Previous |  Up |  Next

Article

Keywords:
$\aleph $-spaces; $g$-metrizable spaces; strong sequence-covering mappings; sequence-covering mappings; mssc-mappings; $\pi $-mappings
Summary:
In this paper, we give the mapping theorems on $\aleph $-spaces and $g$-metrizable spaces by means of some sequence-covering mappings, mssc-mappings and $\pi $-mappings.
References:
[1] A.  Arkhangel’skii: Mappings and spaces. Russian Math. Surveys 21 (1966), 115–162. DOI 10.1070/RM1966v021n04ABEH004169 | MR 0227950
[2] S.  Lin: Locally countable collections, locally finite collections and Alexandroff’s problems. Acta Math. Sinica 37 (1994), 491–496. (Chinese) MR 1337096 | Zbl 0812.54022
[3] S.  Lin: Generalized Metric Spaces and Mappings. Chinese Scientific publ., Beijing, 1995.
[4] L.  Foged: Characterizations of $\aleph $-spaces. Pacific J.  Math. 110 (1984), 59–63. DOI 10.2140/pjm.1984.110.59 | MR 0722737 | Zbl 0542.54030
[5] J.  Nagata: General metric spaces  I. In: Topics in General Topology, North-Holland, Amsterdam, 1989. MR 1053200
[6] F.  Siwiec: Sequence-covering and countably bi-quotient mappings. Gen. Top. Appl. 1 (1971), 143–154. MR 0288737 | Zbl 0218.54016
[7] Y.  Tanaka: Symmetric spaces, $g$-developable spaces and $g$-metrizable spaces. Math. Japonica 36 (1991), 71–84. MR 1093356 | Zbl 0732.54023
[8] F. Siwiec: On defining a space by a weak-base. Pacific J.  Math. 52 (1974), 233–245. DOI 10.2140/pjm.1974.52.233 | MR 0350706 | Zbl 0285.54022
[9] G.  Gruenhage, E.  Michael and Y.  Tanaka: Spaces determined by point-countable covers. Pacific J.  Math. 113 (1984), 303–332. DOI 10.2140/pjm.1984.113.303 | MR 0749538
[10] V. I.  Ponomarev: Axioms of countability and continuous mappings. Bull. Pol. Acad. Math. 8 (1960), 127–133. MR 0116314
[11] P. O’Meara: On paracompactness in function spaces with the compact-open topology. Proc. Amer. Math. Soc. 29 (1971), 183–189. MR 0276919
[12] R. W.  Heath: On open mappings and certain spaces satisfying the first countability axiom. Fund. Math. 57 (1965), 91–96. MR 0179763 | Zbl 0134.41802
[13] J. A.  Kofner: On a new class of spaces and some problems of symmetrizability theory. Soviet Math. Dokl. 10 (1969), 845–848. Zbl 0202.53702
[14] D. K.  Burke: Cauchy sequences in semimetric spaces. Proc. Amer. Math. Soc. 33 (1972), 161–164. DOI 10.1090/S0002-9939-1972-0290328-3 | MR 0290328 | Zbl 0233.54015
[15] K. B.  Lee: On certain $g$-first countable spaces. Pacific J.  Math. 65 (1976), 113–118. DOI 10.2140/pjm.1976.65.113 | MR 0423307 | Zbl 0359.54022
[16] L.  Foged: On $g$-metrizability. Pacific J.  Math. 98 (1982), 327–332. DOI 10.2140/pjm.1982.98.327 | MR 0650013 | Zbl 0478.54025
[17] S.  Lin: A note on the Arens’ space and sequential fan. Topology Appl. 81 (1997), 185–196. DOI 10.1016/S0166-8641(97)00031-X | MR 1485766 | Zbl 0885.54019
[18] S.  Lin: On $g$-metrizable spaces. Chinese Ann. Math. 13 (1992), 403–409. MR 1190593 | Zbl 0770.54030
[19] C.  Liu and M.  Dai: $g$-metrizability and $S_\omega $. Topology Appl. 60 (1994), 185–189. MR 1302472
[20] Y.  Tanaka: $\sigma $-hereditarily closure-preserving $k$-networks and $g$-metrizability. Proc. Amer. Math. Soc. 112 (1991), 283–290. MR 1049850 | Zbl 0770.54031
[21] R. H.  Bing: Metrization of topological spaces. Canad. J.  Math. 3 (1951), 175–186. DOI 10.4153/CJM-1951-022-3 | MR 0043449 | Zbl 0042.41301
Partner of
EuDML logo