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Inductive_dimension abstract "In the mathematical field of topology, the inductive dimension of a topological space X is either of two values, the small inductive dimension ind(X) or the large inductive dimension Ind(X). These are based on the observation that, in n-dimensional Euclidean space Rn, (n − 1)-dimensional spheres (that is, the boundaries of n-dimensional balls) have dimension n − 1. Therefore it should be possible to define the dimension of a space inductively in terms of the dimensions of the boundaries of suitable open sets.The small and large inductive dimensions are two of the three most usual ways of capturing the notion of "dimension" for a topological space, in a way that depends only on the topology (and not, say, on the properties of a metric space). The other is the Lebesgue covering dimension. The term "topological dimension" is ordinarily understood to refer to Lebesgue covering dimension. For "sufficiently nice" spaces, the three measures of dimension are equal.".
Inductive_dimension wikiPageID "3173612".
Inductive_dimension wikiPageLength "5141".
Inductive_dimension wikiPageOutDegree "28".
Inductive_dimension wikiPageRevisionID "650086974".
Inductive_dimension wikiPageWikiLink Boundary_(topology).
Inductive_dimension wikiPageWikiLink Category:Dimension_theory.
Inductive_dimension wikiPageWikiLink Closed_set.
Inductive_dimension wikiPageWikiLink Closure_(topology).
Inductive_dimension wikiPageWikiLink Compact_space.
Inductive_dimension wikiPageWikiLink Euclidean_space.
Inductive_dimension wikiPageWikiLink Georg_Nöbeling.
Inductive_dimension wikiPageWikiLink Hausdorff_space.
Inductive_dimension wikiPageWikiLink Irrational_number.
Inductive_dimension wikiPageWikiLink Ivor_Grattan-Guinness.
Inductive_dimension wikiPageWikiLink Karl_Menger.
Inductive_dimension wikiPageWikiLink Lebesgue_covering_dimension.
Inductive_dimension wikiPageWikiLink Mathematical_induction.
Inductive_dimension wikiPageWikiLink Metric_space.
Inductive_dimension wikiPageWikiLink Metrizable.
Inductive_dimension wikiPageWikiLink Metrization_theorem.
Inductive_dimension wikiPageWikiLink Miroslav_Katětov.
Inductive_dimension wikiPageWikiLink Normal_space.
Inductive_dimension wikiPageWikiLink Open_set.
Inductive_dimension wikiPageWikiLink P._S._Aleksandrov.
Inductive_dimension wikiPageWikiLink Pavel_Alexandrov.
Inductive_dimension wikiPageWikiLink Second-countable_space.
Inductive_dimension wikiPageWikiLink Separable_space.
Inductive_dimension wikiPageWikiLink Sphere.
Inductive_dimension wikiPageWikiLink Subset.
Inductive_dimension wikiPageWikiLink Topological_space.
Inductive_dimension wikiPageWikiLink Topology.
Inductive_dimension wikiPageWikiLink Urysohns_metrization_theorem.
Inductive_dimension wikiPageWikiLinkText "Inductive dimension".
Inductive_dimension wikiPageWikiLinkText "Menger-Nöbeling theorem".
Inductive_dimension wikiPageWikiLinkText "a dimension corresponding to its topology".
Inductive_dimension wikiPageWikiLinkText "embedding theorem".
Inductive_dimension wikiPageWikiLinkText "inductive dimension".
Inductive_dimension hasPhotoCollection Inductive_dimension.
Inductive_dimension wikiPageUsesTemplate Template:Empty_section.
Inductive_dimension wikiPageUsesTemplate Template:Unreferenced.
Inductive_dimension subject Category:Dimension_theory.
Inductive_dimension type Article.
Inductive_dimension type Article.
Inductive_dimension comment "In the mathematical field of topology, the inductive dimension of a topological space X is either of two values, the small inductive dimension ind(X) or the large inductive dimension Ind(X). These are based on the observation that, in n-dimensional Euclidean space Rn, (n − 1)-dimensional spheres (that is, the boundaries of n-dimensional balls) have dimension n − 1.".
Inductive_dimension label "Inductive dimension".
Inductive_dimension sameAs Induktive_Dimension.
Inductive_dimension sameAs Induktív_dimenzió.
Inductive_dimension sameAs 帰納次元.
Inductive_dimension sameAs 귀납적_차원.
Inductive_dimension sameAs m.08x1c7.
Inductive_dimension sameAs Q841816.
Inductive_dimension sameAs Q841816.
Inductive_dimension sameAs 歸納維數.
Inductive_dimension wasDerivedFrom Inductive_dimension?oldid=650086974.
Inductive_dimension isPrimaryTopicOf Inductive_dimension.