Geodesic
Class preserving mappings of equivalence systems
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 61-64

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By an equivalence system is meant a couple $\mathcal{A} = (A,\theta )$ where $A$ is a non-void set and $\theta $ is an equivalence on $A$. A mapping $h$ of an equivalence system $\mathcal{A}$ into $\mathcal{B}$ is called a class preserving mapping if $h([a]_{\theta }) = [h(a)]_{\theta {^{\prime }}}$ for each $a \in A$. We will characterize class preserving mappings by means of permutability of $\theta $ with the equivalence $\Phi _{h}$ induced by $h$.
Classification : 03E02, 08A02, 08A35
Keywords: equivalence relation; equivalence system; relational system; homomorphism; strong homomorphism; permuting equivalences 
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Chajda, Ivan. Class preserving mappings of equivalence systems. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 43 (2004) no. 1, pp. 61-64. http://geodesic.mathdoc.fr/item/AUPO_2004__43_1_a5/