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equivalence relation; equivalence system; relational system; homomorphism; strong homomorphism; permuting equivalences
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 $h$.
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[3] Riguet J.: Relations binaires, fermetures, correspondances de Galois. Bull. Soc. Math. France 76 (1948), 114–155. MR 0028814 | Zbl 0033.00603
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