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In page Moore space (algebraic topology):

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for in, where H n ( X ) {\displaystyle H_{n}(X)} denotes the n-th singular homology group of X and H ~ i ( X ) {\displaystyle {\tilde {H}}_{i}(X)} is the i-th reduced homology group. Then X is said to be a Moore space. Also, X is by definition simply-connected if n>1.[citation needed]