Abstract
Solving a problem of Diestel [9] relevant to the theory of cycle spaces of infinite graphs, we show that the Freudenthal compactification of a locally finite graph can have connected subsets that are not path-connected. However we prove that connectedness and path-connectedness to coincide for all but a few sets, which have a complicated structure.
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Georgakopoulos, A. Connected but not path-connected subspaces of infinite graphs. Combinatorica 27, 683–698 (2007). https://doi.org/10.1007/s00493-007-2188-6
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DOI: https://doi.org/10.1007/s00493-007-2188-6