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### Questions (116)

 10 Show that the countable product of metric spaces is metrizable 10 Prove or Disprove that $\left|\frac{e^{2i\theta} -2e^{i\theta} - 1}{e^{2i\theta} + 2e^{i\theta} -1}\right| = 1$ 8 Show bounded harmonic function on $\mathbb{C}$ is constant. 8 For $I,J$ ideals, show that $IJ\subseteq (I\cap J)(I+J)$ 8 What Topology does a Straight Line in the Plane Inherit as a Subspace of $\mathbb{R_l} \times \mathbb{R}$ and of $\mathbb{R_l} \times \mathbb{R_l}$

### Reputation (2,071)

 +5 Prove that in $\mathbb{R}$, if $|a-b|>\alpha$ for all $a\in A$ and $b\in B$, then outer measure $m^*(A\cup B)=m^*(A)\cup m^*(B)$ +10 Rigorous proof that $\int_{\Omega}X\;dP=\int_{-\infty}^{\infty}xf(x)\;dx$ +5 Show that the countable product of metric spaces is metrizable +10 let $\alpha$ = $\sqrt[3]{2}$ and $K = \Bbb{\alpha}$ factor $x^{3} -2$ into irreducible polynomials in $K(x)$

 4 Is there a matrix $A$ such that $rank(A) < rank(A^2)$? 4 Let $M$ be a maximal ideal in $R$ such that for all $x\in M$, $x+1$ is a unit. Show that $R$ is a local ring with maximal ideal $M$ 4 Accidents of small $n$ 3 What are rings good for? 2 Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$

### Tags (102)

 8 abstract-algebra × 20 3 complex-analysis × 28 4 linear-algebra × 4 3 ring-theory × 4 4 commutative-algebra × 3 2 matrices × 4 4 examples-counterexamples × 2 1 residue-calculus × 3 4 big-list 1 numerical-linear-algebra × 2

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