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 20L13 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

karin.martin@uni-rostock.de
Seite generiert am 18.11.2008,   17:20   Uhr