The size of the chain recurrent set for generic maps on an $n$-dimensional locally $(n-1)$-connected compact space
Tom 119 / 2010
Colloquium Mathematicum 119 (2010), 229-236
MSC: Primary 37B20; Secondary 37C20, 37A05.
DOI: 10.4064/cm119-2-5
Streszczenie
For $n \geq 1$, 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 $f:X \to X$, 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).
