Ends and quasicomponents

• Autorzy: Nikita Shekutkovski , Gorgi Markoski
• 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 $$ EX = \mathop {\lim }\limits_ \leftarrow (Q(X\backslash C)),inclusions,CcompactinX) $$.

Słowa kluczowe

EN

Ends; Quasicomponent; Inverse limit; Covering by disjoint open sets

Kategorie tematyczne

• 54D40: Remainders
• 54E45: Compact (locally compact) metric spaces
• 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)
• 54D45: Local compactness, σ -compactness

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 6
• Strony: 1009-1015

Daty

wydano

2010-12-01

online

2010-10-30

Twórcy

autor

Nikita Shekutkovski

• Sts. Cyril and Methodius University

autor

Gorgi Markoski

• Sts. Cyril and Methodius University

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

Identyfikatory

DOI

10.2478/s11533-010-0069-5