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- Residuated_mapping abstract "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 it is order-preserving: that is, if 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 under f of a principal down-set need not be a principal down-set. If it is, f is called residuated.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.".
- Residuated_mapping wikiPageExternalLink gal_bw.ps.gz.
- Residuated_mapping wikiPageExternalLink primer.ps.
- Residuated_mapping wikiPageID "18272082".
- Residuated_mapping wikiPageLength "6800".
- Residuated_mapping wikiPageOutDegree "31".
- Residuated_mapping wikiPageRevisionID "614748221".
- Residuated_mapping wikiPageWikiLink Antitone.
- Residuated_mapping wikiPageWikiLink Arity.
- Residuated_mapping wikiPageWikiLink Binary_operation.
- Residuated_mapping wikiPageWikiLink Binary_operator.
- Residuated_mapping wikiPageWikiLink Boolean_algebra_(structure).
- Residuated_mapping wikiPageWikiLink Category:Order_theory.
- Residuated_mapping wikiPageWikiLink Ceiling_function.
- Residuated_mapping wikiPageWikiLink Down-set.
- Residuated_mapping wikiPageWikiLink Duality_(order_theory).
- Residuated_mapping wikiPageWikiLink Floor_and_ceiling_functions.
- Residuated_mapping wikiPageWikiLink Floor_function.
- Residuated_mapping wikiPageWikiLink Function_composition.
- Residuated_mapping wikiPageWikiLink Galois_connection.
- Residuated_mapping wikiPageWikiLink Group_(mathematics).
- Residuated_mapping wikiPageWikiLink Identity_function.
- Residuated_mapping wikiPageWikiLink Image_(mathematics).
- Residuated_mapping wikiPageWikiLink Magma_(algebra).
- Residuated_mapping wikiPageWikiLink Matrix_multiplication.
- Residuated_mapping wikiPageWikiLink Monotonic_function.
- Residuated_mapping wikiPageWikiLink Order_(journal).
- Residuated_mapping wikiPageWikiLink Order_dual.
- Residuated_mapping wikiPageWikiLink Ordered_group.
- Residuated_mapping wikiPageWikiLink Ordered_monoid.
- Residuated_mapping wikiPageWikiLink Ordered_semigroup.
- Residuated_mapping wikiPageWikiLink Partially_ordered_group.
- Residuated_mapping wikiPageWikiLink Partially_ordered_set.
- Residuated_mapping wikiPageWikiLink Partially_ordered_sets.
- Residuated_mapping wikiPageWikiLink Pergamon_Press.
- Residuated_mapping wikiPageWikiLink Pointwise.
- Residuated_mapping wikiPageWikiLink Pointwise_order.
- Residuated_mapping wikiPageWikiLink Preimage.
- Residuated_mapping wikiPageWikiLink Principal_down-set.
- Residuated_mapping wikiPageWikiLink Quasigroup.
- Residuated_mapping wikiPageWikiLink Residuated_lattice.
- Residuated_mapping wikiPageWikiLink Springer-Verlag.
- Residuated_mapping wikiPageWikiLink Springer_Science+Business_Media.
- Residuated_mapping wikiPageWikiLink Transpose.
- Residuated_mapping wikiPageWikiLink Transposed_matrix.
- Residuated_mapping wikiPageWikiLink Upper_set.
- Residuated_mapping wikiPageWikiLinkText "Residuated mapping".
- Residuated_mapping wikiPageWikiLinkText "residuated mapping".
- Residuated_mapping hasPhotoCollection Residuated_mapping.
- Residuated_mapping wikiPageUsesTemplate Template:Reflist.
- Residuated_mapping subject Category:Order_theory.
- Residuated_mapping type Field.
- Residuated_mapping comment "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 it is order-preserving: that is, if 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 }.".
- Residuated_mapping label "Residuated mapping".
- Residuated_mapping sameAs m.04cybx2.
- Residuated_mapping sameAs Q7315523.
- Residuated_mapping sameAs Q7315523.
- Residuated_mapping wasDerivedFrom Residuated_mapping?oldid=614748221.
- Residuated_mapping isPrimaryTopicOf Residuated_mapping.