Jianing Song's user avatar
Jianing Song's user avatar
Jianing Song's user avatar
Jianing Song
  • Member for 2 years
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19 votes
0 answers
331 views

Can ($X^I$, product topology) and ($X^I$, box topology) be homeomorphic for some nontrivial $X$ and infinite $I$?

16 votes
1 answer
589 views

If $f:[a,b]\to\mathbb{R}$ continuous at all but countably infinitely many points, $g:[0,1]\to[a,b]$ continuous, can $f\circ g$ be a.e. discontinuous?

13 votes
1 answer
915 views

Do the groups $\operatorname{SL}$, $\operatorname{PGL}$, and $\operatorname{PSL}$ over a field $K$ always have the same automorphism group?

12 votes
3 answers
967 views

How do we compare the set of natural numbers in different models of ZFC

11 votes
1 answer
254 views

What is the $\lim_{n\to\infty}\sinh^{\circ n}\sqrt{\dfrac{3}{n}}$?

11 votes
1 answer
214 views

Can the Petersen graph be embedded into the 3-dimensional Euclidean space such that every edge is a segment and has unit length?

10 votes
0 answers
332 views

Can the Cauchy product of a conditionally convergent series with itself be absolutely convergent?

10 votes
2 answers
414 views

“Every open ball is closed" and "every closed ball is open", does one imply the other?

9 votes
1 answer
262 views

Must a countable disjoint union of closed balls in $\mathbb{R}^n$ with positive radius be disconnected?

8 votes
1 answer
179 views

Why inner regularity of measure is defined as to be approximable from within by compact sets and not by closed sets?

7 votes
1 answer
149 views

Is $\left\{\sqrt{n}\sin^{\circ n}\left(\dfrac{z}{\sqrt{n}}\right)\right\}$ locally uniformly convergent over $\mathbb{C}-\{y{\rm i}:|y|\ge\sqrt{3}\}$?

7 votes
0 answers
103 views

Is there a nonmeasurable subset of $\mathbb{R}^2$ that is $1-$dimensional Hausdorff measurable?

6 votes
1 answer
184 views

If an infinite group $G$ is generated by two elements $a,b$ such that $a^n=b^n=e$, must $x^n=e$ have infinitely many solutions?

6 votes
1 answer
111 views

Sequence of polynomials $\{P_n\}$ of bounded degree such that $\int_{\mathbb{R}^d}P_n(x)\varphi(x){\rm d}x$ converges for all test functions $\varphi$

5 votes
0 answers
141 views

When are two semidirect products of two cyclic groups isomorphic

5 votes
0 answers
90 views

What is the minimal possible value of ${\max_{x\in [0,1]}} |f(x)|$ if $f\in \mathbb{Z}[x]$ is of degree $n$?

5 votes
1 answer
163 views

If $f(x)$ is Henstock-Kurzweil integrable on $[a,b]$, then is $f(x)\mathrm{e}^{\mathrm{i}x}$ also Henstock-Kurzweil integrable on $[a,b]$?

4 votes
1 answer
182 views

Does $\bigcap^{\infty}_{k=0} (I + (X^k)) = I$ hold in a ring of formal power series?

4 votes
1 answer
176 views

If $|\cdot|$ is a nontrivial nonarchimedean absolute value over $\mathbb{C}$, must $(\mathbb{C},|\cdot|)$ embed into $\mathbb{C}_p$ for some $p$?

4 votes
1 answer
98 views

Does $\gcd(x^{p^2+p+1}-1, (x+1)^{p^2+p+1}-1)\neq 1$ in $\mathbb{F}_p[x]$ for all primes $p$?

4 votes
1 answer
64 views

Do we have $\log\Gamma(2x+1)-2\log\Gamma(x+1)\ge\log(x^2+1)$ for $x\in[0,1]$?

4 votes
1 answer
76 views

If $\{\|T^n\|:n\in\mathbb{Z}\}$ is bounded for an invertible operator $T$ over a Hilbert space, must $T$ be conjugate to an orthogonal operator?

4 votes
1 answer
65 views

Positive integer sequence with sum $m$ can have at most $\left\lfloor\dfrac{m^2}{8}\right\rfloor$ increasing pairs

4 votes
1 answer
97 views

Is every compact set in the metric topology closed in the minimal topology containing the closed balls as closed sets?

3 votes
0 answers
46 views

Poincaré's definition of manifolds [duplicate]

3 votes
1 answer
112 views

Step in Yoshida's proof of Hasse-Arf theorem

3 votes
0 answers
48 views

Measure spaces that stabilize with respect to the Carathéodory extension

3 votes
1 answer
45 views

$\Sigma_i a_ib_i = 0$ implies $\Sigma_i \sigma_1(a_i)\sigma_2(b_i) = 0$ for $\sigma_i\in\mathrm{Aut}(F_i),i=1,2$ that agree in $F_1\cap F_2$?

3 votes
3 answers
214 views

Does the derivative of a vector-valued BV function $f(x)$ equal to the norm of $f'(x)$?

3 votes
1 answer
186 views

Product of a derivative and a continuous function is a Darboux function