Proximality in minimal transformation groups

Author:

Shapiro Leonard

Abstract

We present an action of the integers on a compact metric space such that in the resulting minimal topological transformation group the proximal relation is an equivalence relation but is not closed.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference8 articles.

1. On the proximal relation in topological dynamics;Auslander, Joseph;Proc. Amer. Math. Soc.,1960

2. Endomorphisms of minimal sets;Auslander, Joseph;Duke Math. J.,1963

3. Proximity relations in transformation groups;Clay, Jesse Paul;Trans. Amer. Math. Soc.,1963

4. Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation;Furstenberg, Harry;Math. Systems Theory,1967

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1. Topological Aspects of Dynamics of Pairs, Tuples and Sets;Recent Progress in General Topology III;2013-12-12

2. Proximity and distality via Furstenberg families;Topology and its Applications;2006-06

3. The distal order of a minimal flow;Israel Journal of Mathematics;2002-12

4. An inverted tower of almost 1-1 extensions;Journal d'Analyse Mathématique;1984-12

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