Betti number

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(topology, algebraic topology) Any of a sequence of numbers, denoted bₙ, which characterise a given topological space K by giving, for each dimension, the number of holes in K of said dimension; (formally) the rank of the nth homology group, Hₙ, of K.

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The Betti number b_n of a topological space indicates the number of n-dimensional holes it contains.

詳細

意味（1）

(topology, algebraic topology) Any of a sequence of numbers, denoted bₙ, which characterise a given topological space K by giving, for each dimension, the number of holes in K of said dimension; (formally) the rank of the nth homology group, Hₙ, of K.

Poincaré proved that Betti numbers are invariants and used them to extend Euler's polyhedral formula to higher dimensional spaces.

詳細

Betti numbers （ plural ）