Boundaries of coarse proximity spaces and boundaries of compactifications

DOI10.1007/s40879-023-00616-1OpenAlexW2905921704MaRDI QIDQ2699567

Jeremy Siegert, Pawel Grzegrzolka

Publication date: 19 April 2023

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.09802

zbMATH Keywords

compactificationsboundariesproximitycoarse geometryGromov boundaryHigson coronavisual boundarylarge-scale geometrySmirnov compactificationcoarse topologycoarse proximity\(\delta\)-hyperbolic spacescat(0) spacesFreudenthal boundary

Mathematics Subject Classification ID

Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Proximity structures and generalizations (54E05) Remainders in general topology (54D40)

Cites Work

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• Asymptotic resemblance
• Large scale geometry
• An alternative definition of coarse structures
• Coarse proximity and proximity at infinity
• Extension theorems for large scale spaces via coarse neighbourhoods
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• On spaces with connected Higson coronas
• Asymptotic topology
• Metric Compactifications and Coarse Structures
• Asymptotic cones and boundaries of CAT(0) spaces
• Geometric Group Theory
• Normality conditions of structures in coarse geometry and an alternative description of coarse proximities

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