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Homotopy theory, homological algebra, algebraic treatments of manifolds.
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Continuous surjection $S^n\to S^m$, $n<m$ [closed]
I had an exam last week on algebraic topology.
"Suppose $f:S^n\to S^m$ is continuous, where $n<m$. Prove that $f$ is homotopic to a constant mapping. The fact that $S^n$ minus one point is homeomorph …