The regionally proximal relation

Auslander, Joseph; Ellis, David B.; Ellis, Robert

doi:10.1090/S0002-9947-1995-1285970-7

The regionally proximal relation

Authors: Joseph Auslander, David B. Ellis and Robert Ellis
Journal: Trans. Amer. Math. Soc. 347 (1995), 2139-2146
MSC: Primary 54H20
DOI: https://doi.org/10.1090/S0002-9947-1995-1285970-7
MathSciNet review: 1285970
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Sufficient conditions for the regionally proximal relation $Q(X)$ of a minimal flow to be an equivalence relation are obtained in terms of the group $\mathcal {G}(X)$ of the flow and various groups which depend only on the acting group $T$.

Joseph Auslander, Minimal flows and their extensions, North-Holland Mathematics Studies, vol. 153, North-Holland Publishing Co., Amsterdam, 1988. Notas de Matemática [Mathematical Notes], 122. MR 956049
Robert Ellis, Group-like extensions of minimal sets, Trans. Amer. Math. Soc. 127 (1967), 125–135. MR 221492, DOI https://doi.org/10.1090/S0002-9947-1967-0221492-2
Robert Ellis, Lectures on topological dynamics, W. A. Benjamin, Inc., New York, 1969. MR 0267561
Robert Ellis, The Veech structure theorem, Trans. Amer. Math. Soc. 186 (1973), 203–218 (1974). MR 350712, DOI https://doi.org/10.1090/S0002-9947-1973-0350712-1
Robert Ellis, Shmuel Glasner, and Leonard Shapiro, Proximal-isometric ($\scr P\scr J $) flows, Advances in Math. 17 (1975), no. 3, 213–260. MR 380755, DOI https://doi.org/10.1016/0001-8708%2875%2990093-6
Robert Ellis and Harvey Keynes, A characterization of the equicontinuous structure relation, Trans. Amer. Math. Soc. 161 (1971), 171–183. MR 282357, DOI https://doi.org/10.1090/S0002-9947-1971-0282357-4
Douglas C. McMahon, Relativized weak disjointness and relatively invariant measures, Trans. Amer. Math. Soc. 236 (1978), 225–237. MR 467704, DOI https://doi.org/10.1090/S0002-9947-1978-0467704-9
William A. Veech, The equicontinuous structure relation for minimal Abelian transformation groups, Amer. J. Math. 90 (1968), 723–732. MR 232377, DOI https://doi.org/10.2307/2373480

B. L. van der Waerden, Stetigkeitssatz der halbeinfachen Lieschen Gruppen, Math. Z. 161 (1933), 780-786.