Partial actions of groups on profinite spaces

投射有限群的闭子群的计数

Counting the Closed Subgroups of Profinite Groups

投射有限群的闭和闭正规子群的集合带有自然投射有限拓扑.通过结合代数和拓扑方法的大小，这些子群空间的计算，和空间部分分类同胚。

Partial actions of groups on hyperspaces

Let $X$ be a compact Hausdorff space. In this work we translate partial actions of $X$ to partial actions on some hyperspaces determined by $X,$ this gives an endofunctor $2^{-}$ in the category of partial actions on compact Hausdorff spaces which generates a monad in this category. Moreover, structural relations between partial actions $θ$ on $X$ and partial determined by $2^θ$ are established.

零伦等变移位与Borsuk-Ulam相容紧致阿贝尔群

Nullhomotopic equivariant shifts and Borsuk-Ulam-compatible compact abelian groups

本文否证了Borsuk-Ulam风格猜想，指出其仅在无挠profinite紧致阿贝尔群情形下失效，并给出精确刻画。

Borel Globalizations of Partial Actions of Polish Groups

We show that the enveloping space $X_G$ of a partial action of a Polish group $G$ on a Polish space $X$ is a standard Borel space, that is to say, there is a topology $τ$ on $X_G$ such that $(X_G, τ)$ is Polish and the quotient Borel structure on $X_G$ is equal to $Borel(X_G,τ)$. To prove this result we show a generalization of a theorem of Burgess about Borel selectors for the orbit equivalence relation induced by a group action and also show that some properties of the Vaught's transform are valid for partial actions of groups.

A topological correspondence between partial actions of groups and inverse semigroup actions

We present some generalizations of the well-known correspondence, found by R. Exel, between partial actions of a group $G$ on a set $X$ and semigroup homomorphism of $S(G)$ on the semigroup $I(X)$ of partial bijections of $X,$ being $S(G)$ an inverse monoid introduced by Exel. We show that any unital premorphism $θ:G\to S$, where $S$ is an inverse monoid, can be extended to a semigroup homomorphism $θ^*:T\to S$ for any inverse semigroup $T$ with $S(G)\subseteq T\subseteq P^*(G)\times G,$ being $P^*(G)$ the semigroup of non-empty subset of $G$, and such that $E(S)$ satisfies some lattice theore…