Applied General Topology (Oct 2021)
Orbitally discrete coarse spaces
Abstract
Given a coarse space (X, E), we endow X with the discrete topology and denote X ♯ = {p ∈ βG : each member P ∈ p is unbounded }. For p, q ∈ X ♯ , p||q means that there exists an entourage E ∈ E such that E[P] ∈ q for each P ∈ p. We say that (X, E) is orbitally discrete if, for every p ∈ X ♯ , the orbit p = {q ∈ X ♯ : p||q} is discrete in βG. We prove that every orbitally discrete space is almost finitary and scattered.
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