The size of the chain recurrent set for generic maps on an n-dimensional locally (n-1)-connected compact space

Katsuya Yokoi. "The size of the chain recurrent set for generic maps on an n-dimensional locally (n-1)-connected compact space." Colloquium Mathematicae 119.2 (2010): 229-236. <http://eudml.org/doc/284171>.

@article{KatsuyaYokoi2010,
abstract = {For n ≥ 1, given an n-dimensional locally (n-1)-connected compact space X and a finite Borel measure μ 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 μ-measure zero. The same is true for n = 0 (skipping the local connectedness assumption).},
author = {Katsuya Yokoi},
journal = {Colloquium Mathematicae},
keywords = {chair recurrent set; Borel mesure; dimension; locally -connected manifold; Menger manifold},
language = {eng},
number = {2},
pages = {229-236},
title = {The size of the chain recurrent set for generic maps on an n-dimensional locally (n-1)-connected compact space},
url = {http://eudml.org/doc/284171},
volume = {119},
year = {2010},
}

TY - JOUR
AU - Katsuya Yokoi
TI - The size of the chain recurrent set for generic maps on an n-dimensional locally (n-1)-connected compact space
JO - Colloquium Mathematicae
PY - 2010
VL - 119
IS - 2
SP - 229
EP - 236
AB - For n ≥ 1, given an n-dimensional locally (n-1)-connected compact space X and a finite Borel measure μ 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 μ-measure zero. The same is true for n = 0 (skipping the local connectedness assumption).
LA - eng
KW - chair recurrent set; Borel mesure; dimension; locally -connected manifold; Menger manifold
UR - http://eudml.org/doc/284171
ER -