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C_c(X)Spaces with X Locally Compact

C_c(X)Spaces with X Locally Compact
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摘要 In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space Cc （X） has countable tightness [if and only if it has bounding tightness] if and only if it is Frechet-Urysohn, if and only if Cc （X） contains a dense （LM） subspace and if and only if X is a-compact. In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space Cc （X） has countable tightness [if and only if it has bounding tightness] if and only if it is Frechet-Urysohn, if and only if Cc （X） contains a dense （LM） subspace and if and only if X is a-compact.
作者 J.C.FERRANDO S.MOLL
机构地区 Centro de Investigación Operativa Departamento de Matemática Aplicada
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第9期1593-1600,共8页 数学学报（英文版）
关键词 Frechet-Urysohn space countable [bounding] tightness （LM）-space Frechet-Urysohn space, countable [bounding] tightness, （LM）-space
分类号 O189.11 [理学—基础数学]
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参考文献19

  • 1Ferrando, J. C., Kakol, J., Lopez Pellicer, M.: A characterization of distinguished Prechet spaces. Math. Nachr, to appear
  • 2Ferrando, J. C., Kakol, J., Lopez Pellicer, M., Saxon, S.: Tightness and distinguished Frechet spaces. Submitted
  • 3Arkhangel'skii, A. V.: Topological function spaces, Math. and its Appl., Kluwer, 1992
  • 4Pytkeev, E. G.: The tightness of spaces of continuous functions. Russian Math. Surveys, 37, 176-177 (1982)
  • 5Gerlits, J.: Some properties of C (X), II. Topology Appl., 15, 255-262 (1983)
  • 6McCoy, R. A.: k-space function spaces. Intern J. Math., 3, 701-711 (1980)
  • 7Kakol, J., Lopez Pellicer, M.: On countable bounded tightness for spaces Cp (X). J. Math. Anal. Appl., 280, 155-162 (2003)
  • 8Kakol, J., Tweddle, I.: Spaces of continuous functions Cp (X) as (LM)tv-spaces, Bull. Belg. Math. Soc. (Special Volume in Honour of N. De Grande-De Kimpe) 101-108, 2002
  • 9Kothe, G.: Topological vector spaces I, Springer-Verlag, Berlin, Heidelberg, New York, 1983
  • 10Arkhangel'skii, A. V.: A survey on Cp-theory. M. Husek and J. van Mills (Eds.) In: Recent Progress in General Topology, 1-48, 1992
Acta Mathematica Sinica,English Series
2007年 第9期

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