Janson A.J
Reputation
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 3 $f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$ 2 Sphere-sphere intersection is not a surface 1 Prove that invertible metrices set is an open set in a given space, and the determinant is continuous 1 Basic compactness 1 How does one represent a range like $[a,b]$ if the ^range^ is exactly $1$?

### Reputation (140)

 +45 $f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$ +5 Convergence of the series $\sum_{n=1}^{\infty}((1/n)-\sin(1/n))$..? +15 How to define $a^x$? +10 Sphere-sphere intersection is not a surface

### Questions (3)

 4 Convergence of the series $\sum_{n=1}^{\infty}((1/n)-\sin(1/n))$..? 3 How to define $a^x$? 1 Can we generalize the result of Urysohn's lemma to countable collection of pairwise disjoint closed subsets of a normal space..?

### Tags (14)

 7 general-topology × 6 1 matrices 3 real-analysis × 3 0 proof-verification 1 elementary-set-theory 0 compactness 1 linear-algebra 0 divergent-series 1 determinant 0 convergence

### Accounts (5)

 Mathematics 140 rep 6 Stack Overflow 6 rep 2 MathOverflow 6 rep 2 TeX - LaTeX 1 rep 1 Android Enthusiasts 1 rep 2