A closed subgroup $H$ of a locally compact group $G$ is confined if the closure conjugacy class in Chabauty space does not contain trivial subgroup. We establish dynamical criterion on action totally disconnected $X$ ensuring that no relatively amenable can be confined. This property equivalent to fact its Furstenberg boundary free. Our applies Neretin groups. deduce each has two inequivalent i...

In the theory of operator algebras, classification of group actions on approximately finite dimensional (AFD) factors has been done since Connes’s work [2]. In subfactor theory, various results on classification of group actions have been obtained. The most powerful results have been obtained by Popa in [16], who classified the strongly outer actions of discrete amenable groups on strongly amen...

there are several kinds of hyperrings, for example, krasnerhyperrings, multiplicative hyperring, general hyperrings and$h_v$-rings. in a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. in this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf keywords:} multiplic...