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Shant Danielian

### Questions (51)

 11 Continuity together with finite additivity implies countable additivity 7 Show that the boundary of $A$ is empty iff $A$ is closed and open. 7 Show that $u(x)=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right)$ is in $W^{1,n}(U)$, where $U=B(0,1)\subset\mathbb{R}^n$. 7 Prove that any homeomorphism $f:X\to Y$ establishes a bijection between the components of $X$ to the components of $Y$. 5 Show that $S^n\cong\mathbb{R}^n\cup\{\infty\}.$

### Reputation (798)

 +5 Continuity together with finite additivity implies countable additivity +5 Show that $u(x)=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right)$ is in $W^{1,n}(U)$, where $U=B(0,1)\subset\mathbb{R}^n$. +5 Show that the boundary of $A$ is empty iff $A$ is closed and open. +5 Prove that any homeomorphism $f:X\to Y$ establishes a bijection between the components of $X$ to the components of $Y$.

 2 Compact and Connected. 2 Trigonometric Functions. Definite Integrals 2 Basic Calculus Problems. 1 Show that $S^n\cong\mathbb{R}^n\cup\{\infty\}.$ 0 Show that the infinite intersection of nested non-empty closed subsets of a compact space is not empty

### Tags (35)

 4 calculus × 2 2 derivatives 3 general-topology × 30 2 trigonometry 3 compactness × 10 0 proof-verification × 19 2 integration × 3 0 matlab × 9 2 functions × 2 0 notation × 5

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