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Ends and quasicomponents

Nikita Shekutkovski; Gorgi Markoski — 2010

Open Mathematics

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 $E X = lim_{\leftarrow} (S (X ∖ C)), i n c l u s i o n s, C c o m p a c t i n X)$ . 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...

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