# Ends and quasicomponents

Nikita Shekutkovski; Gorgi Markoski

Open Mathematics (2010)

- Volume: 8, Issue: 6, page 1009-1015
- ISSN: 2391-5455

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topNikita Shekutkovski, and Gorgi Markoski. "Ends and quasicomponents." Open Mathematics 8.6 (2010): 1009-1015. <http://eudml.org/doc/269720>.

@article{NikitaShekutkovski2010,

abstract = {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 \[ EX = \mathop \{\lim \}\limits \_ \leftarrow (Q(X\backslash C)),inclusions,CcompactinX) \]
.},

author = {Nikita Shekutkovski, Gorgi Markoski},

journal = {Open Mathematics},

keywords = {Ends; Quasicomponent; Inverse limit; Covering by disjoint open sets; space of ends; inverse limit; quasi-component},

language = {eng},

number = {6},

pages = {1009-1015},

title = {Ends and quasicomponents},

url = {http://eudml.org/doc/269720},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Nikita Shekutkovski

AU - Gorgi Markoski

TI - Ends and quasicomponents

JO - Open Mathematics

PY - 2010

VL - 8

IS - 6

SP - 1009

EP - 1015

AB - 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 \[ EX = \mathop {\lim }\limits _ \leftarrow (Q(X\backslash C)),inclusions,CcompactinX) \]
.

LA - eng

KW - Ends; Quasicomponent; Inverse limit; Covering by disjoint open sets; space of ends; inverse limit; quasi-component

UR - http://eudml.org/doc/269720

ER -

## References

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- [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 Zbl1054.54024

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