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Ussesjskskns
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  • The Cantor Set
17 votes
0 answers
733 views

Does there exist $f:\Bbb{R}\to \Bbb{R}$ additive onto function such that $f(F) \subset \Bbb{R}$ has the property of Baire for every $F$?

14 votes
0 answers
573 views

Is there any condition that makes a measure zero set necessarily countable?

11 votes
1 answer
646 views

Can we define a norm on $\Bbb{R^\omega}$ in a basis free way?

9 votes
1 answer
375 views

Can we find $f\in \Bbb{R}^{[0, 1]}$ with the property $\mathcal{M}$ which doesn't satisfy the property $\mathcal{B}$?

8 votes
1 answer
358 views

Does there any diffentiable function $f$ such that $f'$ is discontinuous exactly on $\Bbb{Q} $ and continuous on $\Bbb{R}\setminus \Bbb{Q}$?

8 votes
3 answers
653 views

Given $G=\langle a\rangle$, $|G|=n$ and $d\mid n$, show $G$ has a unique subgroup of order $d$.

8 votes
2 answers
594 views

Can you give me an example of a non compact topological space with compact dense subset?

7 votes
1 answer
566 views

Is the proof $|d(x, A) - d(y, A) |\le d(x, y) $ in $(X, d) $ and $\emptyset \neq A \subset X$ and $x, y\in X$ logically perfect?

7 votes
3 answers
482 views

Does there exists any non trivial linear metric space in which every open ball is not convex?

5 votes
2 answers
250 views

$\forall f\in Y^X$ with $\text{Gr}(f) $ is closed implies $f\in C(X, Y) $. Does this implies $(Y, \tau_Y) $ is compact?

5 votes
0 answers
282 views

Conjecture: Any two matrices of size $n×n$ with same characteristic and minimal polynomial are similar implies $n\le 3$.

4 votes
1 answer
357 views

Investigating a property related to the biconnected property

4 votes
0 answers
139 views

What condition(s) on $X$ and $A$ can ensure the existence of an element $a\in A$ such that $d(x_0, a)=d(x_0, A) $?

4 votes
3 answers
1k views

What is the intuition behind distributional derivative and why distributional derivative is useful?

4 votes
1 answer
533 views

Prove or disprove : In a topological space $(X,\tau)$ if every compact subsets $K\subset X$ are closed then $(X, \tau) $ is hausdorff.

4 votes
4 answers
618 views

Why do we not avoid the phrase "if we assume AC " and take it as granted?

4 votes
1 answer
161 views

Why was the concept of first/second categories in metric spaces introduced?

3 votes
1 answer
84 views

$f:X \to Y $ is continuous on $X$ and $(X, d_1) $ is compact. Then $f:X\to Y$ is uniformly continuous on $X$

3 votes
2 answers
403 views

Is $d(A, B) =|(A\Delta B)|$ a metric on all finite subsests?

3 votes
1 answer
160 views

Does every uncountable subsets has a limit point implies the topological space is Lindel$\ddot{\text{o}}$f?

3 votes
1 answer
218 views

$\operatorname{tr}(A^k)=0 \space \forall k\in \Bbb{Z}^+$ implies $A$ is nilpotent. Does this imply $\operatorname {char}(K) =0$?

3 votes
1 answer
179 views

A sort of converse of Banach-Steinhaus theorem.

3 votes
1 answer
228 views

Let $\mathcal{B}_0(X, Y)$ is a Banach space. Does this imply that $Y$ is a Banach space?

3 votes
2 answers
188 views

Asking for clarification of a Wikipedia article on uniform continuity

3 votes
0 answers
193 views

Spaces where each compact subset has compact closure: have they already been studied?

3 votes
2 answers
192 views

Classification of all groups up to Isomorphism having no proper non trivial subgroup of finite index.

2 votes
2 answers
447 views

If each subring of the fraction field of an integral domain $\mathcal{R}$ (and properly containing $\mathcal{R}$) is a PID, is $\mathcal{R}$ a PID?

2 votes
1 answer
141 views

Conjecture:A fixed point subset of real numbers are precisely closed and bounded interval.

2 votes
0 answers
82 views

Identify all abelian groups up to Isomorphism having only one non trivial proper subgroup of finite index?

2 votes
1 answer
225 views

What will be the next step to ensure that the pointwise convergence implies convergence in the operator norm?