On the Proximal Relation in Topological Dynamics
نویسندگان
چکیده
منابع مشابه
On the Proximal Relation in Topological Dynamics
Let iX, T) be a transformation group with compact Hausdorff phase space X. The points x and y of A" are said to be proximal provided, whenever ß is a member of the unique compatible uniformity of X, there exists i£ T such that (x/, yt) GßIf x and y are not proximal, they are said to be distal. Let P denote the proximal relation in X. P is a reflexive, symmetric, T invariant relation, but is not...
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Proximal Relations in Topological Dynamics1
Standing notations. Let (X, T, ir) be a transformation group with compact phase space. The proximal relation of (X, T, if) is denoted by P(X) and the syndetically proximal relation by L(X). The product transformation group induced by (X, P, 7r):;will be denoted by (XXX, T, p), which is defined by (x, y)pi = (xirt, yir1) for (x, y) QXXX and tQ T. For simplicity we shall write xt for X7r' and (xt...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1960
ISSN: 0002-9939
DOI: 10.2307/2034433