43 Coffee Break Riddle 30 Which sequences converge in a cofinite topology and what is their limit? 17 Real life applications of Topology 13 Who are some forgotten mathematicians? 12 Ring theory exercises at the graduate level

### Reputation (4,083)

 +10 $f: \mathbf{R} \rightarrow \mathbf{R}$ monotone increasing $\Rightarrow$ $f$ is measurable +10 $f: \mathbb{R}^2-\{0\} \rightarrow \mathbb{R}$ is continuously differentiable and $f(\alpha x) = \alpha^2f(x)$, then $x \cdot \nabla f(x) = 2 f(x)$ +10 If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$ +10 A good quick introduction to Knot Theory?

### Questions (25)

 21 $f: \mathbf{R} \rightarrow \mathbf{R}$ monotone increasing $\Rightarrow$ $f$ is measurable 14 Space of homeomorphisms Homeo$(S^1)$ of $S^1$ deformation retracts onto $O(2)$ 11 Integral closure $\tilde{A}$ is flat over $A$, then $A$ is integrally closed 11 $\int_X |f_n - f| \,dm \leq \frac{1}{n^2}$ for all $n \geq 1$ $\implies$ $f_n \rightarrow f$ a.e. 8 $\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$ [closed]

### Tags (71)

 61 general-topology × 11 35 big-list × 6 49 soft-question × 6 30 convergence-divergence × 5 43 puzzle 17 applications × 2 43 recreational-mathematics 14 elementary-number-theory × 3 38 reference-request × 11 13 linear-algebra × 3

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