A totally bounded uniformity on coarse metric spaces

Abstract

This paper presents a new version of boundary on coarse spaces. The space of ends functor maps coarse metric spaces to uniform topological spaces and coarse maps to uniformly continuous maps.

Coarse Cohomology with twisted Coefficients

“…We wonder if this result will be of any help with understanding coarse spaces. Note that Remark 98 gave rise to the studies in [21].…”

Nonstandard methods in large-scale topology

“…The nonstandard treatment of topological ends can be found in Goldbring [12] and Insall et al [19]. Some conceptions of "the space at infinity" of a coarse space are studied in, e.g., Hartmann [14] and Grzegrzolka and Siegert [13]. The following is an analogous result to [14,Lemma 36].…”

“…Some conceptions of "the space at infinity" of a coarse space are studied in, e.g., Hartmann [14] and Grzegrzolka and Siegert [13]. The following is an analogous result to [14,Lemma 36]. FIN (X))) by [17,Corollary 3.13]…”

Relating asymptotic dimension to Ponomarev's cofinal dimension via coarse proximities

“…The following definition is a slight variation of a definition in [17] to characterize the covering dimension of the boundaries of coarse proximity spaces. A similar definition is given by Hartmann in [10]. Both definitions are based on the definition of a particular kind of cover for small scale proximity spaces defined by Smirnov in [18] to define a dimension function for proximity spaces.…”