Orbitally discrete coarse spaces





coarse space, ultrafilter, orbitally discrete space, almost finitary space, scattered space


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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Author Biography

Igor V. Protasov, Taras Shevchenko National University of Kyiv

Professor, Faculty of Computer Science and Cybernetics


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How to Cite

I. V. Protasov, “Orbitally discrete coarse spaces”, Appl. Gen. Topol., vol. 22, no. 2, pp. 303–309, Oct. 2021.