About: Lebesgue covering dimension

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In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in atopologically invariant way.

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rdf:type	yago:WikicatTopologicalSpaces yago:Abstraction100002137 yago:Attribute100024264 yago:MathematicalSpace108001685 yago:Set107999699 yago:Space100028651
rdfs:label	Topologická dimenze (cs) Lebesguesche Überdeckungsdimension (de) Dimensión de recubrimiento de Lebesgue (es) Lebesgue covering dimension (en) 르베그 덮개 차원 (ko) ルベーグ被覆次元 (ja) Размерность Лебега (ru) 拓撲維數 (zh) Розмірність Лебега (uk)
rdfs:comment	Topologická dimenze (též Lebesguova pokrývací dimenze) topologického prostoru je přirozené číslo, které prostor charakterizuje a které v běžných případech intuitivně odpovídá jiným definicím dimenze. Topologická dimenze n-rozměrného Euklidova prostoru je n, a podobně topologická dimenze n-rozměrné variety je n. U fraktálů se ale topologická dimenze obvykle liší od Hausdorffovy dimenze, která nemusí být celočíselná. První formální definici topologické dimenze zavedl český matematik Eduard Čech na základě dřívějších výsledků Henri Lebesguea. (cs) Die Lebesguesche Überdeckungsdimension (nach Henri Léon Lebesgue) ist eine geometrisch sehr anschauliche, topologische Charakterisierung der Dimension. (de) In mathematics, the Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in atopologically invariant way. (en) En matemáticas, la dimensión de recubrimiento de Lebesgue o dimensión topológica de un espacio topológico es una de las formas diferentes de definir la dimensión del espacio mediante un invariante topológico. (es) 数学の一分野、位相空間論におけるルベーグ被覆次元（ひふくじげん、英: Lebesgue covering dimension）あるいは位相次元（いそうじげん、英: topological dimension）は、位相空間に対して位相不変量となる次元の概念の（いくつかの同値でないものの）うちの一種である。 (ja) 르베그 덮개 차원(-次元, Lebesgue covering dimension) 또는 르베그 피복 차원(-被覆次元)은 위상수학에서 위상 공간에 적당한 으로서의 차원을 주는 한 방법이다. 위상적 차원(topological dimension)이라고도 불린다. (ko) Размерность Лебега или топологическая размерность — размерность, определённая посредством покрытий, важнейший инвариант топологического пространства.Размерность Лебега пространства обычно обозначается . (ru) 拓撲空間的拓撲維數是 n ，若且唯若 n 是最小的整數使得以下陳述成立：對於任意的一個有限開覆蓋，都存在另一個有限開覆蓋，使得是的精細，且內的每個點都只屬於至多 n+1 個的元素。拓撲維數又稱勒貝格維數。圖象化來解釋： (zh) Розмі́рність Ле́бега або топологічна розмірність — розмірність, визначена за допомогою покриттів, найважливіший інваріант топологічного простору. Розмірність Лебега простору , зазвичай позначається . (uk)
foaf:depiction
dcterms:subject	Dimension theory
Wikipage page ID	398886 (xsd:integer)
Wikipage revision ID	1120583833 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Princeton University Press Metacompact space Homeomorphic Unit circle Inductive dimension Topological invariant Mathematics Geometric set cover problem Normal space N-sphere Hausdorff space Eduard Čech Euclidean space Paracompact space Carathéodory's extension theorem Simplicial complex Refinement (topology) Henri Lebesgue Asymptotic dimension Intersection (set theory) Karl Menger Cohomological dimension Homeomorphism Zero-dimensional space Dimension Assouad–Nagata dimension Dimension theory Plane (mathematics) Integer Metric space Open cover Open set Sheaf (mathematics) Union (set theory) Point-finite collection Dimension theory Topological space Unit disk L. S. Pontryagin Springer-Verlag Open (topology) Disjoint set Closed subset dbr:Affine_dimension
Link from a Wikipage to an external page	https://www.maths.ed.ac.uk/~v1ranick/papers/engelking.pdf https://archive.org/details/dimensiontheoryo0000pear
sameAs	Lebesgue covering dimension Lebesgue covering dimension Lebesgue covering dimension Lebesgue covering dimension Lebesgue covering dimension Lebesgue covering dimension Lebesgue covering dimension Lebesgue covering dimension Lebesgue covering dimension Lebesgue covering dimension Lebesgue covering dimension Lebesgue covering dimension
dbp:wikiPageUsesTemplate	dbt:Springer dbt:Cite_book dbt:Cite_journal dbt:Math dbt:More_footnotes dbt:Mvar dbt:Reflist dbt:Sfn

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