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29 Questions

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19	How to learn from proofs?
13	Why is a covering space of a torus $T$ homeomorphic either to $\mathbb{R}^2$, $S^1\times\mathbb{R}$ or $T$?
7	Why is the orthogonal group $\operatorname{O}(2n,\mathbb R)$ not the direct product of $\operatorname{SO}(2n, \mathbb R)$ and $\mathbb Z_2$?
7	Why does $\{(x,y,z): z \ge 0\}-\{(x,y,z): y=0,0\leq z \leq 1\}$ have trivial fundamental group?
6	How to define weak solution for an elliptic PDE with non-zero Dirichlet boundary condition?

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668 Reputation

+15	Why Zorn's Lemma “fails” on nested boxes problem?
+5	How to define weak solution for an elliptic PDE with non-zero Dirichlet boundary condition?
+5	What are the rules for transformation (translation, dilation, etc.) of integral on n-dimensional sphere?
+5	Why is a covering space of a torus $T$ homeomorphic either to $\mathbb{R}^2$, $S^1\times\mathbb{R}$ or $T$?

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2 Answers

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1	How to prove Weyl’s asymptotic law for the eigenvalues of the Dirichlet Laplacian?
0	How to prove $\lim_{n\to\infty}f(nx)=0$ for almost every $x$, given $f:[0,\infty)\to[0,\infty)$ integrable.

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1 pde × 3	0 real-analysis × 4
1 eigenvalues × 2	0 homework × 3
0 abstract-algebra × 5	0 modules × 3
0 algebraic-topology × 5	0 calculus × 3
0 general-topology × 4	0 numerical-methods × 3

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