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- Isomorphism abstract "In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism (or more generally a morphism) that admits an inverse. Two mathematical objects are isomorphic if an isomorphism exists between them. An automorphism is an isomorphism whose source and target coincide. The interest of isomorphisms lies in the fact that two isomorphic objects cannot be distinguished by using only the properties used to define morphisms; thus isomorphic objects may be considered the same as long as one considers only these properties and their consequences.For most algebraic structures, including groups and rings, a homomorphism is an isomorphism if and only if it is bijective.In topology, where the morphisms are continuous functions, isomorphisms are also called homeomorphisms or bicontinuous functions. In mathematical analysis, where the morphisms are differentiable functions, isomorphisms are also called diffeomorphisms.A canonical isomorphism is a canonical map that is an isomorphism. Two objects are said to be canonically isomorphic if there is a canonical isomorphism between them. For example, the canonical map from a finite-dimensional vector space V to its second dual space is a canonical isomorphism; on the other hand, V is isomorphic to its dual space but not canonically in general.Isomorphisms are formalized using category theory. A morphism f : X → Y in a category is an isomorphism if it admits a two-sided inverse, meaning that there is another morphism g : Y → X in that category such that gf = 1X and fg = 1Y, where 1X and 1Y are the identity morphisms of X and Y, respectively.".
- Isomorphism thumbnail One5Root.svg?width=300.
- Isomorphism wikiPageExternalLink when_is_one.pdf.
- Isomorphism wikiPageID "14828".
- Isomorphism wikiPageLength "21364".
- Isomorphism wikiPageOutDegree "130".
- Isomorphism wikiPageRevisionID "682549504".
- Isomorphism wikiPageWikiLink Abstract_algebra.
- Isomorphism wikiPageWikiLink Alexandroff_extension.
- Isomorphism wikiPageWikiLink Algebra.
- Isomorphism wikiPageWikiLink Algebraic_structure.
- Isomorphism wikiPageWikiLink American_football.
- Isomorphism wikiPageWikiLink Ancient_Greek.
- Isomorphism wikiPageWikiLink Antisymmetric_relation.
- Isomorphism wikiPageWikiLink Archie_Manning.
- Isomorphism wikiPageWikiLink Asymmetric_relation.
- Isomorphism wikiPageWikiLink Automorphism.
- Isomorphism wikiPageWikiLink Bertrand_Russell.
- Isomorphism wikiPageWikiLink Bijection.
- Isomorphism wikiPageWikiLink Bijective.
- Isomorphism wikiPageWikiLink Binary_relation.
- Isomorphism wikiPageWikiLink Bisimulation.
- Isomorphism wikiPageWikiLink Canonical_map.
- Isomorphism wikiPageWikiLink Cardinality.
- Isomorphism wikiPageWikiLink Category:Morphisms.
- Isomorphism wikiPageWikiLink Category_(mathematics).
- Isomorphism wikiPageWikiLink Category_theory.
- Isomorphism wikiPageWikiLink Cauchy_sequence.
- Isomorphism wikiPageWikiLink Class_(set_theory).
- Isomorphism wikiPageWikiLink Column_vector.
- Isomorphism wikiPageWikiLink Commutative_diagram.
- Isomorphism wikiPageWikiLink Concrete_category.
- Isomorphism wikiPageWikiLink Continuous_function.
- Isomorphism wikiPageWikiLink Coprime.
- Isomorphism wikiPageWikiLink Coprime_integers.
- Isomorphism wikiPageWikiLink Cybernetics.
- Isomorphism wikiPageWikiLink Cyclic_group.
- Isomorphism wikiPageWikiLink Dedekind_cut.
- Isomorphism wikiPageWikiLink Diffeomorphism.
- Isomorphism wikiPageWikiLink Differentiable_function.
- Isomorphism wikiPageWikiLink Differential_equation.
- Isomorphism wikiPageWikiLink Differential_equations.
- Isomorphism wikiPageWikiLink Dimension_(vector_space).
- Isomorphism wikiPageWikiLink Direct_product_of_groups.
- Isomorphism wikiPageWikiLink Double_dual.
- Isomorphism wikiPageWikiLink Dual_space.
- Isomorphism wikiPageWikiLink Eli_Manning.
- Isomorphism wikiPageWikiLink Equality_(mathematics).
- Isomorphism wikiPageWikiLink Equivalence_class.
- Isomorphism wikiPageWikiLink Equivalence_relation.
- Isomorphism wikiPageWikiLink Exponential_function.
- Isomorphism wikiPageWikiLink Extensional_definition.
- Isomorphism wikiPageWikiLink Field_(mathematics).
- Isomorphism wikiPageWikiLink Finite-dimensional_vector_space.
- Isomorphism wikiPageWikiLink Genealogy.
- Isomorphism wikiPageWikiLink Good_Regulator.
- Isomorphism wikiPageWikiLink Good_regulator.
- Isomorphism wikiPageWikiLink Graph_isomorphism.
- Isomorphism wikiPageWikiLink Graph_theory.
- Isomorphism wikiPageWikiLink Group_(mathematics).
- Isomorphism wikiPageWikiLink Group_homomorphism.
- Isomorphism wikiPageWikiLink Group_isomorphism.
- Isomorphism wikiPageWikiLink Heap_(mathematics).
- Isomorphism wikiPageWikiLink Hilbert_space.
- Isomorphism wikiPageWikiLink Hilbert_spaces.
- Isomorphism wikiPageWikiLink Homeomorphism.
- Isomorphism wikiPageWikiLink Homology_(mathematics).
- Isomorphism wikiPageWikiLink Homology_theory.
- Isomorphism wikiPageWikiLink Homomorphism.
- Isomorphism wikiPageWikiLink Intensional_definition.
- Isomorphism wikiPageWikiLink Introduction_to_Mathematical_Philosophy.
- Isomorphism wikiPageWikiLink Inverse_function.
- Isomorphism wikiPageWikiLink Irreflexive_relation.
- Isomorphism wikiPageWikiLink Isometry.
- Isomorphism wikiPageWikiLink Isomorphism_class.
- Isomorphism wikiPageWikiLink Isomorphism_theorem.
- Isomorphism wikiPageWikiLink John_F._Kennedy.
- Isomorphism wikiPageWikiLink Joseph_Kennedy.
- Isomorphism wikiPageWikiLink Joseph_P._Kennedy,_Sr..
- Isomorphism wikiPageWikiLink Laplace_transform.
- Isomorphism wikiPageWikiLink Linear_map.
- Isomorphism wikiPageWikiLink Logarithm.
- Isomorphism wikiPageWikiLink Logarithm_function.
- Isomorphism wikiPageWikiLink Logical_atomism.
- Isomorphism wikiPageWikiLink Ludwig_Wittgenstein.
- Isomorphism wikiPageWikiLink Mathematical_analysis.
- Isomorphism wikiPageWikiLink Mathematical_object.
- Isomorphism wikiPageWikiLink Mathematical_table.
- Isomorphism wikiPageWikiLink Mathematics.
- Isomorphism wikiPageWikiLink Modular_arithmetic.
- Isomorphism wikiPageWikiLink Morphism.
- Isomorphism wikiPageWikiLink Morphisms.
- Isomorphism wikiPageWikiLink Natural_isomorphism.
- Isomorphism wikiPageWikiLink Natural_transformation.
- Isomorphism wikiPageWikiLink One-point_compactification.
- Isomorphism wikiPageWikiLink Order_isomorphism.
- Isomorphism wikiPageWikiLink Order_theory.
- Isomorphism wikiPageWikiLink Partial_order.
- Isomorphism wikiPageWikiLink Partially_ordered_set.
- Isomorphism wikiPageWikiLink Peyton_Manning.