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What tells rational cohomology about integral cohomology?

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Why do we ask that condition in Kan complex?

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CW complex structure of the projective space $\mathbb{RP}^n$

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Explicit isomorphism $\tilde{H_n}(X)\simeq \tilde{H}_{n+1}(SX)$.

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Proving that a subgroup of a finitely generated abelian group is finitely generated

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Is closure of convex subset of $X$ is again a convex subset of $X$?

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show $2^{2^n} + 1 \equiv 2 \pmod{2^{2^m} + 1} $ with $0<m<n$

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Chern Classes and Stiefel-Whitney Classes

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Show that for any positive integer $n$ there is $x \in [0,1-\frac{1}{n}]$ for which $f(x) = f(x+\frac{1}{n})$

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Prove that $\left\{(x,y)\in \mathbb R^2: \ x^2-xy+y^2-1=0\right\}$ is a closed and bounded set.

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