Product recurrence and distal points
Product recurrence and distal points
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DOI：
10.1090/s0002-9947-1994-1170562-x
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发表时间：
1994
影响因子：
1.3
通讯作者：
J. Auslander;H. Furstenberg
中科院分区：
文献类型：
--
作者：
J. Auslander;H. Furstenberg
在紧半群在紧空间上的作用的背景下研究了回归性。（一个重要的情形是作用群的斯通 - 切赫紧化的作用。）如果半群\(E\)作用在空间\(X\)上，并且\(F\)是\(E\)的一个闭子半群，那么\(X\)中的\(x\)被称为\(F\) - 回归的，如果对于某个\(p\in F\)有\(px = x\)，并且如果每当\(y\)是一个\(F\) - 回归点（在\(E\)作用的某个空间\(Y\)中）时，乘积系统中的点\((x,y)\)是\(F\) - 回归的，则\(x\)被称为乘积\(F\) - 回归的。主要结果是，在某些条件下，一个点是乘积\(F\) - 回归的当且仅当它是一个远端点。
Recurrence is studied in the context of actions of compact semigroups on compact spaces. (An important case is the action of the Stone-tech compactification of an acting group.) If the semigroup E acts on the space X and F is a closed subsemigroup of E, then x in X is said to be Frecurrent if px = x for some p E F, and product F-recurrent if whenever y is an F-recurrent point (in some space Y on which E acts) the point (x, y) in the product system is F-recurrent. The main result is that, under certain conditions, a point is product F-recurrent if and only if it is a distal point.