THE SIZE OF THE CHAIN RECURRENT SET FOR GENERIC MAPS ON AN n-DIMENSIONAL LOCALLY (n-1)-CONNECTED COMPACT SPACE

被引：3

作者：

Yokoi, Katsuya ^{[1
]}

机构：

[1] Shimane Univ, Dept Math, Matsue, Shimane 6908504, Japan

来源：

COLLOQUIUM MATHEMATICUM | 2010年 / 119卷 / 02期

关键词：

chain recurrent set; Borel measure; dimension; locally n-connected; manifold; Menger manifold;

D O I：

10.4064/cm119-2-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For n >= 1, given an n-dimensional locally (n - 1)-connected compact space X and a finite Borel measure mu without atoms at isolated points, we prove that for a generic (in the uniform metric) continuous map f:X -> X, the set of points which are chain recurrent under f has mu-measure zero. The same is true for n = 0 (skipping the local connectedness assumption).

引用

页码：229 / 236

页数：8

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