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## Open Mathematics

2010 | 8 | 6 | 1009-1015
Tytuł artykułu

### Ends and quasicomponents

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Języki publikacji
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 $$EX = \mathop {\lim }\limits_ \leftarrow (Q(X\backslash C)),inclusions,CcompactinX)$$.
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EN
Kategorie tematyczne
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Rocznik
Tom
Numer
Strony
1009-1015
Opis fizyczny
Daty
wydano
2010-12-01
online
2010-10-30
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autor
autor
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