Thin subsets of balleans. (English) Zbl 1207.54010

Lutsenko, Ievgen; Protasov, Igor

Appl. Gen. Topol. 11, No. 2, 89-93 (2010).

A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. In Section 1 the authors define the thin subsets of a ballean and, for every ordinal ballean, characterize the ideal generated by the thin subsets. Groups and metric spaces have natural ballean structures, and consequently in Section 2 they apply the result from Section 1 to these spaces.

Reviewer: Dieter Leseberg (Braunschweig)

MSC:

54A25	Cardinality properties (cardinal functions and inequalities, discrete subsets)
54E25	Semimetric spaces
05A18	Partitions of sets
20F60	Ordered groups (group-theoretic aspects)

Keywords:

ballean; thin subset; ideal; countable group