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Emir's user avatar
Emir's user avatar
Emir
  • Member for 12 years, 4 months
  • Last seen more than 10 years ago
42 votes
1 answer
24k views

Totally bounded, complete $\implies$ compact

34 votes
4 answers
48k views

An open ball is an open set

15 votes
2 answers
27k views

$X$ compact metric space, $f:X\rightarrow\mathbb{R}$ continuous attains max/min

11 votes
2 answers
10k views

If $A$ is compact and $B$ is closed, show $d(A,B)$ is achieved [duplicate]

11 votes
1 answer
11k views

show that a subset of $\mathbb{R}$ is compact iff it is closed and bounded

11 votes
1 answer
9k views

every isometry is a homeomorphism

5 votes
1 answer
1k views

Every Cauchy sequence in $\mathbb{C}$ is bounded

4 votes
2 answers
5k views

Open sets in a metric space

4 votes
1 answer
634 views

intersections of sets in metric spaces

4 votes
3 answers
5k views

Simple Bayes Theorem question

4 votes
3 answers
3k views

$X$ is connected iff $\forall A\subset X,$ $\partial A\neq\emptyset$

3 votes
2 answers
2k views

Masters in Numerical Analysis? [closed]

3 votes
1 answer
2k views

An interval is path connected

3 votes
2 answers
866 views

connected components are connected

3 votes
2 answers
106 views

Show $(A^o)^c=\overline{A^c}$

3 votes
2 answers
156 views

A metric on $\mathbb{C^n}$ [duplicate]

3 votes
1 answer
80 views

sets in $\mathbb{C}$ questions

3 votes
4 answers
1k views

compactness and boundedness

3 votes
1 answer
625 views

assumed distance in metric spaces

3 votes
2 answers
407 views

Prove $C(A)=A\cup\partial A$.

2 votes
1 answer
511 views

uniform continuity in metric space

2 votes
2 answers
2k views

totally bounded metric spaces

2 votes
2 answers
3k views

probability question ("birthday paradox")

2 votes
2 answers
147 views

absolute value problem

2 votes
1 answer
1k views

unit ball question

2 votes
2 answers
2k views

$\mathbb{Q}$ in metric space $(\mathbb{R},d)$ neither open nor closed

2 votes
1 answer
75 views

$f(x)=x^n,n\in\mathbb{N}$, exists unique $a$ s.t. $a^n=b$

2 votes
5 answers
6k views

an open ball in $\mathbb{R^n}$ is connected

2 votes
1 answer
189 views

prove $\mathbb{N}$ is complete w.r.t. $d_2$

2 votes
2 answers
318 views

$A$ is open $\iff$ $A\cap\partial A=\emptyset$