Geodesic
Quasiorders, Tolerance Relations and Corresponding “Partitions”
Bulletin of the Section of Logic, Tome 45 (2016) no. 2

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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 [5] are proved in a much more simple way. The third kind of “partition” corresponding to tolerances, not occurring in [5], is introduced.
Keywords: partition, quasiorder, tolerance relation 
@article{BSL_2016_45_2_a3,
     author = {Nowak, Marek},
     title = {Quasiorders, {Tolerance} {Relations} and {Corresponding} {{\textquotedblleft}Partitions{\textquotedblright}}},
     journal = {Bulletin of the Section of Logic},
     publisher = {mathdoc},
     volume = {45},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BSL_2016_45_2_a3/}
}
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Nowak, Marek. Quasiorders, Tolerance Relations and Corresponding “Partitions”. Bulletin of the Section of Logic, Tome 45 (2016) no. 2. http://geodesic.mathdoc.fr/item/BSL_2016_45_2_a3/