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Pedro Gomes
  • Member for 5 years, 8 months
  • Last seen more than a month ago
10 votes
2 answers
11k views

Continuous bijection between compact and Hausdorff spaces is a homeomorphism

6 votes
1 answer
248 views

Doubt about the convergence of $\displaystyle \sum_k^{n-1}f(\frac{k+\theta} n)-n\int_0^1 f(x)\,dx$

6 votes
8 answers
4k views

Prove $\sum\limits_{n=1}^\infty \ln({1+\frac 1 {{n}}})$ is divergent. [duplicate]

5 votes
4 answers
6k views

Prove $\sum\limits_{n=2}^\infty \frac {1} {n\ln(n)\ln\ln{n}}$ is divergent. [duplicate]

5 votes
2 answers
302 views

$f_n\to f$ then $\phi(x)=Ce^x$?

4 votes
3 answers
5k views

Proving every metrizable space is normal space

4 votes
3 answers
684 views

Understanding the proof $C(X)$ is complete

4 votes
3 answers
197 views

Compute $\lim_{n\to\infty}\int_\limits{0}^{\infty}\frac{dx}{x^{n}+1}$

4 votes
2 answers
613 views

Questions about proof of Raabe's test in Wikipedia

4 votes
1 answer
3k views

What is a regular submanifold?

4 votes
1 answer
3k views

Polygonally connected open sets

4 votes
3 answers
9k views

Proof that $W^{\perp\perp}=W$ (in a finite dimensional vector space) [duplicate]

3 votes
1 answer
239 views

$V=V^*$? the dual space

3 votes
2 answers
200 views

$A,B$ same eigenvalue $\lambda$

3 votes
1 answer
1k views

Pointwise and Uniform convergence intuition and examples

3 votes
2 answers
1k views

Infinite countable Union of $\sigma-\text{Algebras}$ exercise

3 votes
2 answers
119 views

$X_1\times_h...\times_hX_{n-1}=\sqrt{\det(H)}H^{-1}[\det([E_1\:X])...\det([E_{n-1}\:X]]^t$ derivation

3 votes
4 answers
83 views

$Z=\{(x,y)\in\mathbb{R}^2:x>0,y=\frac{1}{x}\}$ closed in $\mathbb{R}^2$?

3 votes
1 answer
192 views

$\int_\limits{1}^{\infty}\frac{\cos x}{x^{\alpha}}dx$ diverges or converges?

3 votes
2 answers
2k views

Is the kernel of the adjoint operator equal to the kernel of the operator ($\ker (A)=\ker (A')$)?

3 votes
5 answers
114 views

Find the convergence domain of the series $\sum_\limits{n=1}^{\infty}\frac{(-1)^{n-1}}{n3^n(x-5)^n}$

3 votes
1 answer
117 views

$I(\alpha)=\int_\limits{0}^{\infty}\frac{\sin(\alpha x)}{x}dx$

3 votes
1 answer
71 views

Study the convergence of $\sum_\limits{n=1}^{\infty}\frac{(-1)^n}{(x+n)^p}$

3 votes
1 answer
39 views

How $\lim_{n\to\infty}\frac{|x|}{(1+x^{2n})^{\frac{1}{n}}}=\frac{1}{|x|}\lim_{n\to\infty}\frac{1}{(1+\frac{1}{2^n})^{\frac{1}{n}}}$?

3 votes
0 answers
447 views

Proving every compact space is locally compact.

3 votes
3 answers
2k views

$\sqrt{|xy|}$ verifies the Cauchy-Riemann equations at $(0,0)$, but is not differentiable at $(0,0)$

3 votes
1 answer
55 views

Proving $f_n(z)=\frac{nz}{1+n^3z^2}$ converges uniformly

3 votes
1 answer
165 views

Showing there is a unique invariant measure on the unit circumference

3 votes
4 answers
5k views

An example of open but not closed map.

3 votes
3 answers
2k views

Show that $\mathbb{R}$ is Hausdorff.

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