Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Equivalent_definitions_of_mathematical_structures> ?p ?o }
- Equivalent_definitions_of_mathematical_structures abstract "In mathematics, equivalent definitions are used in two somewhat different ways. First, within a particular mathematical theory (for example, Euclidean geometry), a notion (for example, ellipse or minimal surface) may have more than one definition. These definitions are equivalent in the context of a given mathematical structure (Euclidean space, in this case). Second, a mathematical structure may have more than one definition (for example, topological space has at least 7 definitions; ordered field has at least 2 definitions).In the former case, equivalence of two definitions means that a mathematical object (for example, geometric body) satisfies one definition if and only if it satisfies the other definition.In the latter case, the meaning of equivalence (between two definitions of a structure) is more complicated, since a structure is more abstract than an object. Many different objects may implement the same structure.".
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- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Adjacency_matrix.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Affine_space.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Affine_transformation.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Banach_space.
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- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Bijection.
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- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Cartesian_product.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Category:Mathematical_structures.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Category_theory.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Characterizations_of_the_category_of_topological_spaces.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Complex_number.
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- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Conformal_geometry.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Conformal_map.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Constructor_(object-oriented_programming).
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Cryptomorphism.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Diffeomorphism.
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- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Fixed_point_(mathematics).
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Function_(mathematics).
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- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Graph_isomorphism.
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- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Hilbert_space.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Homeomorphism.
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- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink If_and_only_if.
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- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Metric_space.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Minimal_surface.
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- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Order_isomorphism.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Ordered_field.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Partially_ordered_set.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Peano_axioms.
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- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Structure_(category_theory).
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- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Symplectic_manifold.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Symplectomorphism.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Topological_group.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Topological_space.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Topological_vector_space.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Type_theory.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Uniform_isomorphism.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Uniform_space.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Unitary_transformation.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Vector_space.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Von_Neumann–Bernays–Gödel_set_theory.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Equivalent_definitions_of_mathematical_structures wikiPageWikiLinkText "Equivalent definitions of mathematical structures".
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