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Ends and Tangles
Diestel, Reinhard...

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Ends and Tangles by Diestel, Reinhard ( Author )
Lemonjar Open Access
N.A
14-10-2015
We show that an arbitrary infinite graph can be compactified by its ℵ0-tangles in much the same way as the ends of a locally finite graph compactify it in its Freudenthal compactification. In general, the ends then appear as a subset of its ℵ0-tangles. The ℵ0-tangles of a graph are shown to form an inverse limit of the ultrafilters on the sets of components obtained by deleting a finite set of vertices. The ℵ0-tangles that are ends are precisely the limits of principal ultrafilters. The ℵ0-tangles that correspond to a highly connected part, or ℵ0-block, of the graph are shown to be precisely those that are closed in the topological space of its finite-order separations.
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Article
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36.88 KB
English
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MYR 0.00
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https://arxiv.org/abs/1510.04050
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