| 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 $x\in X$.