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2010 | 8 | 6 | 1009-1015
Tytuł artykułu

Ends and quasicomponents

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EN
Abstrakty
EN
Let X be a connected locally compact metric space. It is known that if X is locally connected, then the space of ends (Freudenthal ends), EX, can be represented as the inverse limit of the set (space) S(X C) of components of X C, i.e., as the inverse limit of the inverse system $$ EX = \mathop {\lim }\limits_ \leftarrow (S(X\backslash C)),inclusions,CcompactinX) $$. In this paper, the above result is significantly improved. It is shown that for a space which is not locally connected, we can replace the space of components by the space of quasicomponents Q(X C) of X C. The following result is proved: if X is a connected locally compact metric space, then $$ EX = \mathop {\lim }\limits_ \leftarrow (Q(X\backslash C)),inclusions,CcompactinX) $$.
Twórcy
Bibliografia
  • [1] Ball B.J., Proper shape retracts, Fund. Math., 89(2), 1975, 177–189
  • [2] Ball B.J., Quasicompactifications and shape theory, Pacific J. Math., 84(2), 1979, 251–259
  • [3] Dugundji J., Topology, Series in Advanced Mathematics, Allyn and Bacon, Boston, 1966
  • [4] Engelking R., General Topology, 2nd ed., Sigma Ser. Pure Math., 6, Heldermann, Berlin, 1989
  • [5] Hocking J.G., Young G.S., Topology, Addison-Wesley, Reading-London, 1961
  • [6] Kuratowski K., Topology, Vol. 2, Mir, Moscow, 1969 (in Russian)
  • [7] Michael E., Cuts, Acta Math., 111(1), 1964, 1–36 http://dx.doi.org/10.1007/BF02391006
  • [8] Shekutkovski N., Vasilevska V., Equivalence of different definitions of space of ends, God. Zb. Inst. Mat. Prir.-Mat. Fak. Univ. Kiril Metodij Skopje, 39, 2001, 7–13
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-010-0069-5
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