Quasiorders, Tolerance Relations and Corresponding “Partitions”
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The paper deals with a generalization of the notion of partition for wider classes of binary relations than equivalences: for quasiorders and tolerance relations. The counterpart of partition for the quasiorders is based on a generalization of the notion of equivalence class while it is shown that such a generalization does not work in case of tolerances. Some results from  are proved in a much more simple way. The third kind of “partition” corresponding to tolerances, not occurring in , is introduced.