Zoltán Boros
Árpád Száz

Reflexivity, Transitivity, Symmetry, and Anti-Symmetry of the Intersection Convolution of Relations

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 63, 55 - 62 (2008)

MSC: 04A05  
  44A35   Convolution
  46A22   Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]
ZDM: -  
CR: -  
PACS: -  

Abstract:   We give some sufficient conditions in order that the intersection convolution $F\ast G$ of two relations $F$ and $G$ on a groupoid $X$ be reflexive, transitive, symmetric, and anti-symmetric. Here, $F\ast G$ is a relation on $X$ such that \[ \bigl(\,F\ast G\,\bigr)(x)=\,\bigcap \,\ \bigl\{\,F\,(u)+G\,(v)\,: \qquad x=u+v\,, \quad F\,(u)\ne \emptyset\,, \quad G\,(v)\ne \emptyset\,\bigr\} \] for all $x\in X$.

Keywords:   Groupoids, binary relations, intersection convolution, reflexivity, transitivity, symmetry, and anti-symmetry

Seite generiert am 18.11.2008,   17:20   Uhr