# the symplectic camel

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 29 Coffee Break Riddle 11 Which sequences converge in a cofinite topology and what is their limit? 10 Real life applications of Topology 10 Classical texts that should not be missing from any shelf 10 Who are some forgotten mathematicians?

# 2,289 Reputation

 +5 If $||\mathbf{J}_f(x) - I_n|| < \frac{1}{2n}$ for all $x \in \mathbb{R^n}$, then $f$ is a diffeomorphism +10 Coffee Break Riddle +15 If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$ +5 Convergence of monotone $f_n:[0, \infty) \rightarrow [0,1]$ to continuous, monotone $g$ is uniform

# 22 Questions

 11 Space of homeomorphisms Homeo$(S^1)$ of $S^1$ deformation retracts onto $O(2)$ 10 $\int_X |f_n - f| \,dm \leq \frac{1}{n^2}$ for all $n \geq 1$ $\implies$ $f_n \rightarrow f$ a.e. 6 $\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain 6 Tautological vector bundle over $G_1(\mathbb{R^2})$ isomorphic to the Möbius bundle 5 Example of a finitely generated flat module which is not free

# 68 Tags

 29 recreational-mathematics 13 reference-request × 12 29 puzzle 12 elementary-number-theory × 3 28 general-topology × 10 11 convergence × 5 28 soft-question × 7 10 applications × 2 23 big-list × 8 10 math-history × 2

# 10 Accounts

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