Quasinormal subrelations of ergodic equivalence relations

Outer automorphism groups of some ergodic equivalence relations

Let R a be countable ergodic equivalence relation of type II1 on a standard probability space (X,μ). The group Out R of outer automorphisms of R consists of all invertible Borel measure preserving maps of the space which map R-classes to R-classes modulo those which preserve almost every R-class. We analyze the group Out R for relations R generated by actions of higher rank lattices, providing ...

Global Aspects of Ergodic Group Actions and Equivalence Relations

FUZZY SUBGROUPS AND CERTAIN EQUIVALENCE RELATIONS

In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a...

Relations and Equivalence Relations

In this section, we shall introduce a formal definition for the notion of a relation on a set. This is something we often take for granted in elementary algebra courses, but is a fundamental concept in mathematics i.e. the very notion of a function relies upon the definition of a relation. Following this, we shall discuss special types of relations on sets. 1. Binary Relations and Basic Definit...

Equivalence relations

A motivating example for equivalence relations is the problem of constructing the rational numbers. A rational number is the same thing as a fraction a/b, a, b ∈ Z and b 6= 0, and hence specified by the pair (a, b) ∈ Z× (Z−{0}). But different ordered pairs (a, b) can define the same rational number a/b. In fact, a/b and c/d define the same rational number if and only if ad = bc. One way to solv...