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 3 $\mathbb{P}^1$ is homeomorphic to $\mathbb{S}^2$ 3 What is the integral of function $f(x) = (\sin x)/x$ 3 Application of inverse function theorem? Implicit function theorem? 2 For any element $g$ of $G,$ where $g$ has order $2,$ define $gH=\{gh│h∈H\}$. Prove that the set $K=H∪gH$ is a subgroup of $G.$ 2 Question on homotopy of maps

Reputation (733)

 +70 Algebraic Topology Challenge: Homology of an Infinite Wedge of Spheres +25 Multiples of an irrational number forming a dense subset +5 Induced map on homology from a covering space isomorphism +10 For any element $g$ of $G,$ where $g$ has order $2,$ define $gH=\{gh│h∈H\}$. Prove that the set $K=H∪gH$ is a subgroup of $G.$

Questions (14)

 58 Algebraic Topology Challenge: Homology of an Infinite Wedge of Spheres 19 Multiples of an irrational number forming a dense subset 7 Induced map on homology from a covering space isomorphism 5 Maps that preserve tensor rank 5 Visualizing a Deformation Retraction

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 6 calculus × 3 2 geometry × 2 4 algebraic-topology × 5 2 abstract-algebra × 2 3 general-topology × 3 2 integration × 2 3 real-analysis × 2 2 abelian-groups 2 triangle × 2 2 proof-verification

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