Correspondingly, a set formula_56 has a "descriptive strong inclusion" in a set formula_57 associated with formula_123 (denoted by formula_261), provided formula_262, "i.e.", formula_263 (formula_264 is far from the complement of formula_257). Let formula_266 be a descriptive formula_1-neighbourhood relation defined by  That is, formula_261, provided the description of each formula_270 is contained in the set of descriptions of the points formula_271. Now observe that any formula_106 in the proximal relator space formula_50 such that formula_155 have disjoint formula_123-neighbourhoods, "i.e.",   A consideration of strong containment of a nonempty set in another set leads to the study of hit-and-miss topologies and the Wijsman topology. Let formula_12 be a real number greater than zero. In the study of sets that are proximally near within some tolerance, the set of proximity relations formula_189 is augmented with a pseudometric tolerance proximity relation (denoted by formula_281) defined by  Let formula_283. In other words, a nonempty set equipped with the proximal relator formula_284 has underlying structure provided by the proximal relator formula_189 and provides a basis for the study of tolerance near sets in formula_50 that are near within some tolerance. Sets formula_106 in a descriptive pseudometric proximal relator space formula_288 are tolerance near sets ("i.e.", formula_289), provided  Relations with the same formal properties as similarity relations of sensations considered by Poincaré are nowadays, after Zeeman, called "tolerance relations". A "tolerance formula_291 on a set formula_292" is a relation formula_293 that is reflexive and symmetric. In algebra, the term "tolerance relation" is also used in a narrow sense to denote reflexive and symmetric relations defined on universes of algebras that are also compatible with operations of a given algebra, "i.e.", they are generalizations of congruence relations (see "e.g.",). In referring to such relations, the term "algebraic tolerance" or the term "algebraic tolerance relation" is used. Transitive tolerance relations are equivalence relations. A set formula_292 together with a tolerance formula_291 is called a "tolerance space" (denoted formula_296).