The fundamental group of a locally finite graph with ends: a hyperfinite approach
Abstract
The end compactification || of the locally finite graph is the union of the graph and its ends, endowed with a suitable topology. We show that π1(||) embeds into a nonstandard free group with hyperfinitely many generators, i.e. an ultraproduct of finitely generated free groups, and that the embedding we construct factors through an embedding into an inverse limit of free groups, recovering a result of Diestel and Spr\"ussel.
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