Издательство: | Книга по требованию |
Дата выхода: | июль 2011 |
ISBN: | 978-6-1312-6005-6 |
Объём: | 92 страниц |
Масса: | 160 г |
Размеры(В x Ш x Т), см: | 23 x 16 x 1 |
High Quality Content by WIKIPEDIA articles! In mathematics, the concept of a residuated mapping arises in the theory of partially ordered sets. It refines the concept of a monotone function. If A, B are posets, a function f: A ? B is defined to be monotone if and only if it is order-preserving: that is, x ? y implies f(x) ? f(y). This is equivalent to the condition that the preimage under f of every down-set of B is a down-set of A. We define a principal down-set to be one of the form ?{b} = { b' ? B : b' ? b }. In general the preimage of a principal down-set need not be a principal down-set. The notion of residuated map can be generalized to a binary operator (or any higher arity) via component-wise residuation. This approach gives rise to notions of left and right division in a partially ordered magma, additionally endowing it with a quasigroup structure. (One speaks only of residuated algebra for higher arities). A binary (or higher arity) residuated map is usually not residuated as a unary map.
Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.