# James

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 30 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?

# 2,330 Reputation

 +10 Coffee Break Riddle +5 If $a \frac{\partial}{\partial x} (f+g) = \sin(f-g)$ and $f= f_0 + af_1 + a^2 f_2 + a^3 f_3+…$, then finding $f_0, f_1, f_2$ and $f_3$ +10 If $f: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ smooth, $g(x,y)= x^3 + y^3$ and $g \circ f \equiv 0$, then $\det Df \equiv 0$ +5 If $f: U \rightarrow \mathbb{R}^n$ differentiable such that $|f(x)-f(y)| \geq c |x-y|$ for all $x,y \in U$, then $\det \mathbf{J}_f(x) \neq 0$

# 25 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

# 71 Tags

 30 recreational-mathematics 13 reference-request × 12 30 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

# 11 Accounts

 Mathematics 2,330 rep 835 MathOverflow 131 rep 5 TeX - LaTeX 121 rep 4 Arqade 116 rep 15 Ask Ubuntu 101 rep 2