Orbitally discrete coarse spaces.

Given a coarse space (X, Ɛ), we endow X with the discrete topology and denote X# = {p 2 G: each member P 2 p is unbounded }. For p, q 2 X#, p||q means that there exists an entourage E 2 E such that E[P] 2 q for each P 2 p. We say that (X, Ɛ) is orbitally discrete if, for every p 2 X#, the orbit p = {q 2 X#: p||q} is discrete in G. We prove that every orbitally discrete space is almost finitary and scattered. [ABSTRACT FROM AUTHOR]