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- W3208496601 abstract "Gray and Kambites introduced a notion of hyperbolicity in the setting of semimetric spaces like digraphs or semigroups. We carry over some of the fundamental results of hyperbolic spaces to this new setting. In particular, we prove under some small additional geometric assumption that their notion of hyperbolicity is preserved by quasi-isometries. We also construct a boundary based on quasi-geodesic rays and anti-rays that is preserved by quasi-isometries and, in the case of locally finite digraphs, refines their ends. We show that it is possible to equip the space, if it is finitely based, with its boundary with a pseudo-semimetric and show some further results for the boundary. We also apply our results to semigroups and give a partial solution to a problem of Gray and Kambites." @default.
- W3208496601 created "2021-11-08" @default.
- W3208496601 creator A5056612439 @default.
- W3208496601 date "2021-10-25" @default.
- W3208496601 modified "2023-09-27" @default.
- W3208496601 title "Hyperbolicity in semimetric spaces, digraphs and semigroups" @default.
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