2019/07/23 by Pawel Grzegrzolka, Grzegrzolka, Pawel, Jeremy Siegert +1
Mathematics · #54D35 #54D40 #54E05 #54F45 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #General Topology (math.GN) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1907.09687
openalex publication_date 2019/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
In this paper, we generalize Dranishnikov's asymptotic inductive dimension to the setting of coarse proximity spaces. We show that in this more general context, the asymptotic inductive dimension of a coarse proximity space is bigger or equal to the inductive dimension of its boundary, and consequently may be strictly bigger than the covering dimension of the boundary. We also give a condition, called complete traceability, on the boundary of the coarse proximity space under which the asymptotic inductive dimension of a coarse proximity space and the inductive dimension of its boundary coincide. Finally, we show that spaces whose boundaries are Z-sets and spaces admitting metrizable compactifications have completely traceable boundaries.