### Questions (798)

 106 Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$ [closed] 38 To show that the set point distant by 1 of a compact set has Lebesgue measure $0$ 30 Why is the determinant $M_n(\mathbb R) \to \mathbb R$ continuous? 26 countable group, uncountably many distinct subgroup? 21 How to show path-connectedness of $GL(n,\mathbb{C})$

### Reputation (17,571)

 +5 $A$ be a $5\times 5$ real matrix $\ni$ each row sum is $1$, then each row sum of the matrix $A^3$? +5 confused in the term “closed” in closed subgroup +5 Does there exist an analytic function such that $|f(z)|=|\sin z|$? -2 Krylov-Bogolioubov Theorem

### Answers (268)

 37 Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$ 17 $AB-BA=I$ having no solutions 11 $I-AB$ be invertible $\Leftrightarrow$ $I-BA$ is invertible 11 Continuous images of Cauchy sequences are not necessarily Cauchy 11 If $2^x=3^y=6^{-z}$ then prove that:$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0$

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