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Moore space (algebraic topology) : ウィキペディア英語版
Moore space (algebraic topology)
:''See also Moore space for other meanings in mathematics.''
In algebraic topology, a branch of mathematics, Moore space is the name given to a particular type of topological space that is the homology analogue of the Eilenberg–Maclane spaces of homotopy theory.
==Formal definition==
Given an abelian group ''G'' and an integer ''n'' ≥ 1, let ''X'' be a CW complex such that
:H_n(X) \cong G
and
:\tilde_i(X) \cong 0
for ''i'' ≠ ''n'', where ''H''''n''(''X'') denotes the ''n''-th singular homology group of ''X'' and \tilde_i(X) is the ''i''th reduced homology group. Then ''X'' is said to be a Moore space.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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