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Algebraic topology front page
Homotopy theory front page
How to compute the (co)homology of a space
How to compute the fundamental group of a space
If your topological invariant takes integer values, they may well be homology classes in disguise
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Littlewood-Paley heuristic for derivative
Littlewood-Paley heuristic
Geometric view of Hölder's inequality
Diagonal arguments
Finding an interval for rational numbers with a high denominator
Try to prove a stronger result
Use self-similarity to get a limit from an inferior or superior limit.
Prove a consequence first
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