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1 2010

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Ends and quasicomponents

100%

Shekutkovski N. , Markoski G.

tom 8

nr 6

1009-1015

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 $$ EX = \mathop {\lim }\limits_ \leftarrow (Q(X\backslash C)),inclusions,CcompactinX) $$.