$\mathbb Z$ -作用的Ellis半群的完全正则性
Complete regularity of Ellis semigroups of $\mathbb Z$-actions
摘要：
证明了紧致全不连通的空间上的$\mathbb Z$ -作用的Ellis半群是完全正则的当且仅当前向逼近性与前向渐近性一致，后向逼近性与后向渐近性一致.进一步证明了前向邻近和后向邻近为传递关系的$\mathbb Z$ -或$\mathbb R$ -作用的Ellis半群至多有两个左极小理想.最后，引入了Ellis半群的近单性概念，并与上述概念相联系。
英文摘要：
It is shown that the Ellis semigroup of a $\mathbb Z$-action on a compact totally disconnected space is completely regular if and only if forward proximality coincides with forward asymptoticity and backward proximality coincides with backward asymptoticity. Furthermore, the Ellis semigroup of a $\mathbb Z$- or $\mathbb R$-action for which forward proximality and backward proximality are transitive relations is shown to have at most two left minimal ideals. Finally, the notion of near simplicity of the Ellis semigroup is introduced and related to the above.
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