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 . 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 .
@article{bwmeta1.element.doi-10_2478_s11533-010-0069-5,
author = {Nikita Shekutkovski and Gorgi Markoski},
title = {Ends and quasicomponents},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {1009-1015},
zbl = {1213.54034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0069-5}
}
Nikita Shekutkovski; Gorgi Markoski. Ends and quasicomponents. Open Mathematics, Tome 8 (2010) pp. 1009-1015. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0069-5/
[1] Ball B.J., Proper shape retracts, Fund. Math., 89(2), 1975, 177–189 | Zbl 0321.55029
[2] Ball B.J., Quasicompactifications and shape theory, Pacific J. Math., 84(2), 1979, 251–259 | Zbl 0394.54020
[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 | Zbl 1054.54024