A tree-of-tangles theorem for infinite tangles

arxiv（2022）

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摘要

Carmesin has extended Robertson and Seymour’s tree-of-tangles theorem to the infinite tangles of locally finite infinite graphs. We extend it further to the infinite tangles of all infinite graphs. Our result has a number of applications for the topology of infinite graphs, such as their end spaces and their compactifications.

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关键词

Infinite tree of tangles,End,Ultrafilter tangle,Tree set,Critical vertex set,distinguish,Efficiently,Collectionwise normal

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