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JonSK
  • Member for 6 years, 7 months
  • Last seen more than 6 years ago
71 votes
1 answer
22k views

Let $X$ be an infinite dimensional Banach space. Prove that every Hamel basis of X is uncountable.

  • 877
35 votes
3 answers
20k views

Total ordering on complex numbers

  • 5,319
28 votes
3 answers
11k views

Generalisation of Dominated Convergence Theorem

26 votes
6 answers
30k views

Why: A holomorphic function with constant magnitude must be constant.

  • 5,045
20 votes
6 answers
16k views

If $\int_0^x f \ dm$ is zero everywhere then $f$ is zero almost everywhere

  • 2,135
17 votes
1 answer
5k views

Show that if $|f(z)| \leq M |z|^n$ then $f$ is a polynomial max degree n

  • 223
15 votes
1 answer
5k views

Zeta function zeros and analytic continuation

  • 1,853
15 votes
2 answers
8k views

The graph of a smooth real function is a submanifold

12 votes
1 answer
5k views

The measure of the image of a set of measure zero

  • 251
8 votes
1 answer
917 views

Proving that:$\int_X f_n g \, d\mu \to \int_X fg \, d\mu$ for all $g$ in $\mathscr{L}^q (X)$

  • 6,894
8 votes
1 answer
777 views

Showing that $|f(z)| \leq \prod \limits_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|$

  • 167
7 votes
2 answers
3k views

Proving $f$ has at least one zero inside unit disk

  • 1,606
7 votes
2 answers
2k views

Intersection of Connected Sets

  • 1,879
6 votes
1 answer
3k views

Strict inequality for Fatou's lemma

  • 4,227
4 votes
1 answer
202 views

Sorgenfrey line is not orderable [closed]

  • 1,651
4 votes
2 answers
5k views

Fatou's Lemma Counterexample

4 votes
1 answer
4k views

Stereographic projection is a homeomorphism $S^n \setminus \{p\} \to \mathbb{R}^n$

  • 8,403
4 votes
1 answer
322 views

Prove a group action is wandering

  • 336
3 votes
1 answer
142 views

If $\mu(A_n)\to 0$ then $\int_{A_n}f\to 0$

  • 565
2 votes
3 answers
112 views

If $f(i)=2i$, then what will be $f(1)$? [duplicate]

  • 1,213
2 votes
1 answer
512 views

The boundary of a closed subset $A$ of a compact connected hausdorff space

2 votes
1 answer
128 views

If each $X_n$ is countably compact then so is $\displaystyle\prod_{n\in\mathbb{N}}X_n$.

  • 1,150
2 votes
0 answers
466 views

Why $M=\{(x, |x|), x\in\mathbb{R}\}$ is not an embedded submanifold?

  • 29
1 vote
1 answer
500 views

Smoothing Lemma

  • 988