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## Fundamenta Mathematicae

2012 | 217 | 1 | 1-12
Tytuł artykułu

### A class of spaces that admit no sensitive commutative group actions

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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.
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1-12
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2012
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• Institute of Mathematics, Shantou University, Shantou, Guangdong, 515063, P.R. China
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• Department of Mathematics, Soochow University, Suzhou, Jiangsu, 215006, P.R. China
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