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Mapping theorems on spaces with sn-network g-functions

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Języki publikacji
EN
Abstrakty
EN
Let Δ be the sets of all topological spaces satisfying the following conditions. (1) Each compact subset of X is metrizable; (2) There exists an sn-network g-function g on X such that if xn → x and yn Є g(n, xn) for all n Є N, then x is a cluster point of {yn}. In this paper, we prove that if X Є Δ, then each sequentially-quotient boundary-compact map on X is pseudo-sequence-covering; if X Є Δ and X has a point-countable sn-network, then each sequence-covering boundary-compact map on X is 1-sequence-covering. As the applications, we give that each sequentially-quotient boundary-compact map on g-metrizable spaces is pseudo-sequence-covering, and each sequence-covering boundary-compact on g-metrizable spaces is 1-sequence-covering.
Rocznik
Tom
Strony
199--208
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • Department of Mathematics Da Nang University, Vietnam
Bibliografia
  • [1] An T.V., Tuyen L.Q., Further properties of 1-sequence-covering maps, Comment. Math. Univ. Carolin., 49(3)(2008), 477-484.
  • [2] Arhangel’skii A.V., Mappings and spaces, Russian Math. Surveys, 21(4)(1966), 115-162.
  • [3] Boone J.R., Siwiec F., Sequentially quotient mappings, Czech. Math. J., 26(1976), 174-182.
  • [4] Engelking R., General Topology (revised and completed edition), Heldermann Verlag, Berlin, 1989.
  • [5] Franklin S.P., Spaces in which sequences suffice, Fund. Math., 57(1965), 107-115.
  • [6] Gao Z., Metrizability of spaces and weak base g-functions, Topology Appl., 146-147(2005), 279-288.
  • [7] Ge Y., Characterizations of sn-metrizable spaces, Publ. Inst. Math., Nouv. Ser., 74(88)(2003), 121-128.
  • [8] Ikeda Y., Liu C., Tanaka Y., Quotient compact images of metric spaces, and related matters, Topology Appl., 122(2002), 237-252.
  • [9] Lee K.B., On certain g-first countable spaces, Pacific J. Math., 65(1)(1976), 113-118.
  • [10] Lin F.C., Lin S., On sequence-covering boundary compact maps of metric spaces, Adv. Math. (China), 39(1)(2010), 71-78.
  • [11] Lin F.C., Lin S., Sequence-covering maps on generalized metric spaces, in: arXiv: 1106.3806.
  • [12] Lin S., On sequence-covering s-mappings, Adv. Math. (China), 25(6)(1996), 548-551.
  • [13] Lin S., Liu C., On spaces with point-countable cs-networks, Topology Appl., 74(1996) 51-60.
  • [14] Lin S., A note on sequence-covering mappings, Acta Math. Hungar., 107(2005), 193-197.
  • [15] Lin S., Yan P., Sequence-covering maps of metric spaces, Topology Appl., 109(2001) 301-314.
  • [16] Mohamad A.m., Conditions which imply metrizability in some generalized metric spaces, Topology Proc., 24(Spring)(1999), 215-232.
  • [17] Siwiec F., On defining a space by a weak base, Pacific J. Math., 52(1974), 233-245.
  • [18] Tanaka Y., Ge Y., Around quotient compact images of metric spaces, and symmetric spaces, Houston J. Math., 32(1)(2006), 99-117.
  • [19] Yan P., On strong sequence-covering compact mappings, Northeastern Math. J., 14(1998), 341-344.
  • [20] Yan P., Lin S., CWC-mappings and metrization theorems, Adv. Math. (China), 36(2)(2007), 153-158.
  • [21] Xia S., Characterizations of certain g-first countable spaces, Adv. Math., 29(2000), 61-64.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ecbb0557-b27a-4039-be5f-b073176fdf1c
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