A class of spaces that admit no sensitive commutative group actions

Jiehua Mai, and Enhui Shi. "A class of spaces that admit no sensitive commutative group actions." Fundamenta Mathematicae 217.1 (2012): 1-12. <http://eudml.org/doc/282816>.

@article{JiehuaMai2012,
abstract = {We show that a metric space X admits no sensitive commutative group action if it satisfies the following two conditions: (1) X has property S, that is, for each ε > 0 there exists a cover of X which consists of finitely many connected sets with diameter less than ε; (2) X contains a free n-network, that is, there exists a nonempty open set W in X having no isolated point and n ∈ ℕ such that, for any nonempty open set U ⊂ W, there is a nonempty connected open set V ⊂ U such that the boundary $∂_X(V)$ contains at most n points. As a corollary, we show that no Peano continuum containing a free dendrite admits a sensitive commutative group action. This generalizes some previous results in the literature.},
author = {Jiehua Mai, Enhui Shi},
journal = {Fundamenta Mathematicae},
keywords = {Sensitivity; expansivity; commutative group action; Peano continuum; dendrite},
language = {eng},
number = {1},
pages = {1-12},
title = {A class of spaces that admit no sensitive commutative group actions},
url = {http://eudml.org/doc/282816},
volume = {217},
year = {2012},
}

TY - JOUR
AU - Jiehua Mai
AU - Enhui Shi
TI - A class of spaces that admit no sensitive commutative group actions
JO - Fundamenta Mathematicae
PY - 2012
VL - 217
IS - 1
SP - 1
EP - 12
AB - We show that a metric space X admits no sensitive commutative group action if it satisfies the following two conditions: (1) X has property S, that is, for each ε > 0 there exists a cover of X which consists of finitely many connected sets with diameter less than ε; (2) X contains a free n-network, that is, there exists a nonempty open set W in X having no isolated point and n ∈ ℕ such that, for any nonempty open set U ⊂ W, there is a nonempty connected open set V ⊂ U such that the boundary $∂_X(V)$ contains at most n points. As a corollary, we show that no Peano continuum containing a free dendrite admits a sensitive commutative group action. This generalizes some previous results in the literature.
LA - eng
KW - Sensitivity; expansivity; commutative group action; Peano continuum; dendrite
UR - http://eudml.org/doc/282816
ER -