论文标题
$ \ Mathbb z $ Actions的Ellis Semigroups的完全规律性
Complete regularity of Ellis semigroups of $\mathbb Z$-actions
论文作者
论文摘要
结果表明，在紧凑的完全断开空间上的$ \ mathbb z $ Action的Ellis Semigroup完全是规律的，并且仅当前向近端与前向渐近性和向后的近端重合与后退渐近性相吻合时。此外，$ \ mathbb z $的Ellis Semigroup或$ \ Mathbb r $ - action的远端近端和向后近端是及时关系，最多有两个最小的理想。最后，引入了Ellis Semigroup几乎简单的概念，并与上述有关。
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.
