Operations preserving equivalence relations

Abstract

In 2014, Cégielski, Grigorieff and Guessarian characterized unary self-maps on the set $\mathbb{Z}$ of integers which preserve all congruences of the additive group. In this note, we propose a shorter and straigthforward proof. We replace this result in the frame of universal algebra.

14 pages

Cited by in corpus (2)

• Generalized metric spaces. Relations with graphs, ordered sets and automata : A survey
• Preservation of discrete structures. A metric point of view