Sumanta's user avatar
Sumanta's user avatar
Sumanta's user avatar
Sumanta
  • Member for 5 years, 5 months
  • Last seen this week
15 votes

Retraction of the Möbius strip to its boundary

11 votes
Accepted

Let $f:\mathbb{R}\to(0,\infty)$ be a differentiable function. For all $x\in\mathbb{R}$ $f'(x)=f(f(x)).$ Then show that such function does not exists

10 votes

Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.

6 votes
Accepted

How to show that $hkh^{-1}\in K$?

6 votes
Accepted

$\det(I+A)=1+\operatorname{Tr}(A)$ if $\operatorname{rank}(A)=1$

6 votes
Accepted

On a finite measure space, can we bound $\lVert f\rVert_1$ given $\lVert f\rVert_2$?

6 votes
Accepted

Lebesgue - Radon - Nikodym Theorem: Question about $\sigma$-finite case

6 votes
Accepted

Uncountably many disjoint dense subsets in $\Bbb{R}$

6 votes
Accepted

Existence of a self-homeomorphism $\phi$ of a connected Hausdorff manifold satisfying $\phi(x)=y$

6 votes
Accepted

On a cw complex structure on the $2$- sphere

5 votes
Accepted

Classify all abelian groups of order $2^4 \cdot 5^2 \cdot 11^3$.

5 votes
Accepted

Dose convergence in integral and measure imply convergence in L

5 votes

Homeomorphism between $S^1×S^1$ and $S^2$

5 votes
Accepted

Prove $(\mathbb{Z} \times \mathbb{Z})/ \langle (2,3)\rangle$ is isomorphic to $\mathbb{Z}$.

5 votes

infimum, supremum of the sequence $\{\sin n\}$

5 votes
Accepted

Let $f$ be integrable on $[a,b]$ and suppose for each integrable function $g$ defined on $[a,b]$, $\int^{b}_afg=0$, then $f(x)=0,\forall x\in[a,b]$

4 votes
Accepted

Let H be a Sylow p-subgroup of G. Prove that H is the only Sylow p-subgroup of G contained in N(H).

4 votes
Accepted

Exercise 6.L - The Elements of Integration and Lebesgue Measure by Bartle

4 votes

Let $X$ be a countable set. Then which of the following are true?

4 votes

Show that ${\rm Aut}(Z_2 \times Z_2) \cong S_3$

4 votes

Limit of : $\lim\limits_{n\to\infty}{(\sqrt[3]{n+1}-\sqrt[3]{n})}$.

4 votes
Accepted

Prove: $\sum b_n < \infty \Longrightarrow \sum a_n < \infty \ $, where $ \ \exists N: \forall n \geq N: \frac{a_{n+1}}{a_n} \leq \frac{b_{n+1}}{b_n}$

4 votes

Prove that a ring with 48 elements is not an integral domain

4 votes
Accepted

How to prove $L^{\infty}(\mathbb R) \cap L^{1} (\mathbb R) \subset L^{2}(\mathbb R)$

4 votes
Accepted

Prove that if $|f(z)| \geq |f(z_{0})|$ then $f(z_{0})=0$

4 votes
Accepted

Fundamental group of a topological group: Inversion

4 votes
Accepted

Every smooth $n$-manifold is diffeomorphic to a properly embedded submanifold of $\mathbb{R}^{2n+1}$.

4 votes
Accepted

Showing if $f$ is Borel measurable and $B$ is a Borel set, then $f^{-1}(B)$ is a Borel set.

4 votes
Accepted

Prove that $d$ is an eigenvalue of $T$

4 votes
Accepted

Is the set of extended natural numbers compact?

1
2 3 4 5
10