A class of spaces that admit no sensitive commutative group actions

• Autorzy: Jiehua Mai , Enhui Shi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54H20: Topological dynamics
• 54F50: Spaces of dimension ≤ 1 ; curves, dendrites

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 217
• Numer: 1
• Strony: 1-12

Daty

wydano

2012

Twórcy

autor

Jiehua Mai

• Institute of Mathematics, Shantou University, Shantou, Guangdong, 515063, P.R. China

autor

Enhui Shi

• Department of Mathematics, Soochow University, Suzhou, Jiangsu, 215006, P.R. China

Identyfikatory

DOI

10.4064/fm217-1-1