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trisct
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11 votes
3 answers
367 views

If $\pi:X\to Y$ is a surjective local homeomorphism and $X$ is a smooth manifold, then does $Y$ become a smooth manifold?

5 votes
1 answer
247 views

What is the Sobolev space of maps between surfaces?

4 votes
0 answers
205 views

The hyperbolic metric on the punctured disk induced by a covering by the upper plane

4 votes
2 answers
188 views

Prove $F[x]/(x^n)$ is an injective module

4 votes
1 answer
305 views

Questions about a proof of the Gauss-Bonnet theorem

4 votes
0 answers
147 views

If $f$ is a $0$-form and $dx$ a $1$-form, then does $f\ dx=f\wedge dx$?

4 votes
1 answer
416 views

Let $x$ be transcendental over $F$. Let $y=f(x)/g(x)$ be a rational function. Prove $[F(x):F(y)]=\max(\deg f,\deg g)$

4 votes
3 answers
151 views

Prove or disprove that the sum is bounded by a constant

3 votes
2 answers
76 views

For random variables $X,Y\in L^1$, if $E[X|\sigma(Y)]=Y$ and $E[Y|\sigma(X)]=X$, prove that $X=Y$ a.s.

3 votes
2 answers
259 views

Let $(X,Y)$ be a Gaussian random vector with given means, variances and correlation, determine $E[X\mid X+Y]$ and $E[X\mid Y]$

3 votes
0 answers
37 views

True or false: a chain of at most countable sets has an at most countable union. [duplicate]

3 votes
1 answer
145 views

Prove that for local rings $R,S$, $M_m(R)\cong M_n(S)\implies R\cong S$ and $m=n$

3 votes
0 answers
719 views

A paradigm of finding all irreducible representations for small groups?

3 votes
2 answers
183 views

Prove that the integral $\int\frac{\tau(s)}{\kappa(s)}ds=0$

3 votes
1 answer
59 views

Show that any monomorphism and a homomorphism can be embedded into a commutative diagram with exact rows.

3 votes
1 answer
192 views

About the concept of a valuation ring

3 votes
2 answers
392 views

The notation $\frac{\partial}{\partial x}$

3 votes
1 answer
234 views

Understanding Teichmuller equivalence of marked compact Riemann surfaces

3 votes
1 answer
61 views

Show that a conformal equivalence of two tori lifts to an automorphism of $\mathbb C$

3 votes
2 answers
291 views

Does a Markov chain with Gaussian transitions $p(x_t|x_{t-1})=\mathcal N(\sqrt{1-\beta_t}x_{t-1},\beta_tI)$ tend to $\mathcal N(0,I)$?

2 votes
1 answer
61 views

Why does the probability function of a Bernoulli variable $X\sim Bern(p)$ have the form $f(x|p)=p^x(1-p)^{1-x}$?

2 votes
0 answers
29 views

Does the derivative of the Fourier series $\sum_{k\geq2}\frac{1}{k^2\log k}\cos kt$ exist?

2 votes
0 answers
80 views

Let $A$ be symmetric and positive definite. Suppose $A=LL^T$ is its Cholesky decomposition. Prove that $||A||_2=||L||_2^2$.

2 votes
0 answers
193 views

What does "pullback" mean in general?

2 votes
2 answers
622 views

Under what circumstances compact $\iff$ closed and bounded

2 votes
1 answer
134 views

How to pronounce $C^\infty$?

2 votes
2 answers
228 views

About the definition of a Riemannian metric

2 votes
2 answers
100 views

Topological basis of a manifold

2 votes
1 answer
42 views

Trouble understanding the proof of global continuation of functions on a manifold

2 votes
0 answers
155 views

About ramification groups