Exercise 3.3.13. Let \(X\) be an anima with a CW-structure.
- (1)
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If \(X\) has no \(n\)-cells, then \(H_n(X) = 0\).
- (2)
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If \(X\) has \(k\) cells in dimension \(n\), then \(H_n(X)\) is generated by at most \(k\) elements.
- (3)
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If \(X\) has no two cells in adjacent dimensions, then \(H_n(X)\) is free abelian with rank equal to the number of \(n\)-cells.
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