Reflexive relations | Symmetric relations | Universal algebra | Lattice theory | Approximations

Tolerance relation

In universal algebra and lattice theory, a tolerance relation on an algebraic structure is a reflexive symmetric relation that is compatible with all operations of the structure. Thus a tolerance is like a congruence, except that the assumption of transitivity is dropped. On a set, an algebraic structure with empty family of operations, tolerance relations are simply reflexive symmetric relations. A set that possesses a tolerance relation can be described as a tolerance space. Tolerance relations provide a convenient general tool for studying indiscernibility/indistinguishability phenomena. The importance of those for mathematics had been first recognized by Poincaré. (Wikipedia).

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Rough set | Graph (discrete mathematics) | Algebraic structure | Vector space | Quotient set | Symmetric relation | Cover (topology) | Modular lattice | Lattice (order) | Group (mathematics) | Zorn's lemma | Congruence relation | Universal algebra | Distributive lattice | Direct product | Binary relation | Transitive relation | Equivalence class | Reflexive relation | Set (mathematics) | Partition of a set | Henri Poincaré | Dependency relation | Ring (mathematics) | Variety (universal algebra) | Boolean algebra | Quasitransitive relation | Module (mathematics)