Equivalence Relations in Sets

Equivalence relation - Wikipedia, the free encyclopedia

In mathematics, an equivalence relation is, loosely, a binary relation on a set that specifies how to split up (i.e. partition) the set into subsets such that every element of the larger set is in e...
en.wikipedia.org/wiki/Equivalence_relation

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Equivalence class - Wikipedia, the free encyclopedia

In mathematics, given a set X and an equivalence relation ~ on X , the equivalence class of an element a in X is the subset of all elements in X which are equivalent to a : The notion of...
en.wikipedia.org/wiki/Equivalence_class

Equivalence Relation

Math reference, building equivalence classes. ... Sets, Equivalence Relation ... A relation possessing all three properties is called an equivalence relation. The relation partitions the set S into disjoint subsets called equivalence classes. When r is an equivalence relation, a simpler function q carries the same information.

www.mathreference.com/set,rst.html www.mathreference.com/set,rst.html

An absorption theorem for minimal AF equivalence relations on Cantor

We prove that a ‘small’ extension of a minimal AF equivalence relation on a Cantor set is orbit equivalent to the AF relation. By a ‘small’ extension we mean an equivalence relation generated by the minimal AF equivalence relation and another ... Keywords: Cantor sets; orbit equivalence; minimal dynamical systems...

projecteuclid.org/euclid.jmsj/1225894037

Réunion d'été 2005 de la SMC/SCHPM

JOHN C. MAYER, University of Alabama at Birmingham; Thurston laminations of the unit disk, equivalence relations, and polynomial Julia sets [ PDF]

www.cms.math.ca/Reunions/ete05/abs/gta.html

Approximating Sets with Equivalence Relations. | D2R Server

rdfs:label Approximating Sets with Equivalence Relations. (xsd:string) ... swrc:pages 145-152 (xsd:string)

dblp.l3s.de/d2r/resource/publications/journals/tcs/Mare... dblp.l3s.de/d2r/resource/publications/journals/tcs/MarekR86

Topological Structures of Rough Sets Induced by Equivalence

rdfs:label Topological Structures of Rough Sets Induced by Equivalence Relations. (xsd:string) ... swrc:pages 621-624 (xsd:string)

dblp.l3s.de/d2r/resource/publications/journals/jaciii/K... dblp.l3s.de/d2r/resource/publications/journals/jaciii/KondoD06

Citations: EQUIVALENCE RELATIONS WITH AMENABLE LEAVES - Goodman,

S. E. Goodman, J. F. Plante, Holonomy and averaging in foliated sets, J. Diff. Geom. 14 (1979), 401--407. EQUIVALENCE RELATIONS WITH AMENABLE LEAVES 13 ... S. E. Goodman, J. F. Plante, Holonomy and averaging in foliated sets, J. Diff. Geom. 14 (1979), 401--407. EQUIVALENCE RELATIONS WITH AMENABLE LEAVES 13;

citeseer.ist.psu.edu/context/418906/0

CiteSeerX - Document Details (Isaac Councill, Lee Giles): Fuzzy set theory is based on a `fuzzification' of the predicate 2 (element of), the concept of membership degrees is considered as fundamental. ... 4 Foundations of fuzzy sets, ... 2 The Mutual Defineability of Fuzzy Equivalence Relations and Fuzzy Partitions – Thiele,

citeseer.ist.psu.edu/94147.html

Equivalence relations

Each equivalence relation on a set partitions the set into its equivalence classes but also for each partition of the set there is an equivalence relation whose equivalence classes are the sets in the partition. ... Next: Congruence modulo n Up: NOTES ON RELATIONS Previous: Relations on a set...

www.math.csusb.edu/notes/rel/node3.html