User Jhon Doe

13 votes

2 answers

4k views

Subset of totally bounded set is totally bounded.

asked Feb 26, 2018 at 3:27

8 votes

3 answers

1k views

$\mathbb{Q}(\alpha)=\mathbb{Q}(\beta)$ if $\alpha, \beta$ are algebraic over $\mathbb{Q}$ of degree $2$ and $\alpha +\beta$ is a root of a quadratic.

asked Oct 15, 2018 at 13:59

7 votes

2 answers

864 views

If $ U$ is maximal among non-principal ideals show that $U$ is prime. (Hints?)

asked Mar 3, 2018 at 4:03

6 votes

4 answers

2k views

Proof of Uncountable Basis for $\mathbb{N} \to \mathbb{R}$ over $\mathbb{R}$

asked Feb 12, 2017 at 14:13

5 votes

2 answers

3k views

Uncountable basis of vector space of infinite sequences in R [duplicate]

asked Feb 12, 2017 at 3:36

5 votes

1 answer

445 views

Prove that no ordinal is an element of itself

asked Nov 6, 2017 at 0:03

5 votes

2 answers

168 views

Counter-example: If $J$ is prime then $f^{-1} (J) $ is prime. $f$ need not be unital.

asked Feb 17, 2018 at 17:05

5 votes

3 answers

1k views

Does a field extension $L$ of $F$ have the same characteristic as $F$?

asked Oct 1, 2018 at 9:09

5 votes

1 answer

959 views

Addition of continuous functions over topological spaces is continuous.

asked Apr 16, 2019 at 14:22

5 votes

0 answers

75 views

Limit of sequence of Riemann integrable functions is not Riemann integrable.

asked Aug 30, 2020 at 9:03

5 votes

1 answer

316 views

If $(X_n)_{n\in \mathbb{N}}$ is a martingale s.t. $\sup_n E[|X_n|]\leq M < \infty$, then $\sum_{n\geq 2}(X_n-X_{n-1})^2<\infty$ almost surely.

asked Feb 23, 2021 at 11:13

4 votes

1 answer

114 views

Independence of functions of independent random variables.

asked Feb 24, 2021 at 4:01

4 votes

1 answer

240 views

Prime Ideal Properly Contained in principal Ideal.

asked May 3, 2018 at 9:54

4 votes

2 answers

233 views

If $\alpha,\beta\in C$ are algebraic over $Q$, show that $\alpha+\beta$ is a root of a quadratic polynomial in $Q[x]$ (with conditions).

asked Oct 15, 2018 at 11:06

4 votes

0 answers

661 views

Using Cauchy's Criterion to show non-uniform convergence of series of functions.

asked Oct 27, 2017 at 17:36

3 votes

1 answer

1k views

Restriction of Continuous Functions is Continuous (Epsilon-Delta)

asked Oct 23, 2017 at 13:18

3 votes

1 answer

126 views

Is $\limsup |C_n|^{\frac{1}{n}} = \limsup |C_{n+j}|^{\frac{1}{n}}? $ where $j\geq0 $

asked Aug 16, 2018 at 0:31

3 votes

1 answer

70 views

Elements in non-Abelian simple Groups.

asked Aug 15, 2019 at 2:19

3 votes

1 answer

535 views

Pullback of pushforward $\sigma$-algebra

asked Aug 22, 2019 at 12:50

3 votes

1 answer

225 views

Extended real line is 2nd Countable (Clarification).

asked Aug 29, 2019 at 15:06

3 votes

1 answer

259 views

What are the approximate eigenvalues of the right shift operator $R$ on $\ell_\infty$

asked Mar 18, 2019 at 11:09

3 votes

0 answers

174 views

Rearrangement of Absolutely convergent series of series.

asked Oct 16, 2019 at 5:12

3 votes

1 answer

142 views

Trouble understanding definition of complex logarithm of Dirichlet L function.

asked Feb 28, 2020 at 6:44

3 votes

2 answers

272 views

If $X_n$ is an $L_1$-bounded martingale, show that $\sum_n(X_n-X_{n-1})^2< \infty$ a.s.

asked Feb 25, 2021 at 7:33

3 votes

1 answer

137 views

Clarification on a solution for Atiyah-Macdonald Chapter 1 Q.3.

asked May 27, 2020 at 16:00

2 votes

1 answer

176 views

Soft Question: Texts for introduction into Complex/Analytic Geometry i.e. GAGA theorems, Several Complex variables.

asked May 9, 2020 at 7:50

2 votes

1 answer

62 views

Explanation of Cardinal Arithmetic Used in Proving that bases of Vector spaces have the same cardinality.

asked Jun 14, 2020 at 15:44

2 votes

0 answers

35 views

Are free Artinian modules finitely generated?

asked Jul 5, 2020 at 15:43

2 votes

0 answers

58 views

Using Martingales to find expected values.

asked Feb 24, 2021 at 19:08

2 votes

0 answers

151 views

Show that integral operator of positive definite kernel is positive.

asked Mar 10, 2021 at 12:32

Stack Exchange Network

198 Questions

Subset of totally bounded set is totally bounded.

$\mathbb{Q}(\alpha)=\mathbb{Q}(\beta)$ if $\alpha, \beta$ are algebraic over $\mathbb{Q}$ of degree $2$ and $\alpha +\beta$ is a root of a quadratic.

If $ U$ is maximal among non-principal ideals show that $U$ is prime. (Hints?)

Proof of Uncountable Basis for $\mathbb{N} \to \mathbb{R}$ over $\mathbb{R}$

Uncountable basis of vector space of infinite sequences in R [duplicate]

Prove that no ordinal is an element of itself

Counter-example: If $J$ is prime then $f^{-1} (J) $ is prime. $f$ need not be unital.

Does a field extension $L$ of $F$ have the same characteristic as $F$?

Addition of continuous functions over topological spaces is continuous.

Limit of sequence of Riemann integrable functions is not Riemann integrable.

If $(X_n)_{n\in \mathbb{N}}$ is a martingale s.t. $\sup_n E[|X_n|]\leq M < \infty$, then $\sum_{n\geq 2}(X_n-X_{n-1})^2<\infty$ almost surely.

Independence of functions of independent random variables.

Prime Ideal Properly Contained in principal Ideal.

If $\alpha,\beta\in C$ are algebraic over $Q$, show that $\alpha+\beta$ is a root of a quadratic polynomial in $Q[x]$ (with conditions).

Using Cauchy's Criterion to show non-uniform convergence of series of functions.

Restriction of Continuous Functions is Continuous (Epsilon-Delta)

Is $\limsup |C_n|^{\frac{1}{n}} = \limsup |C_{n+j}|^{\frac{1}{n}}? $ where $j\geq0 $

Elements in non-Abelian simple Groups.

Pullback of pushforward $\sigma$-algebra

Extended real line is 2nd Countable (Clarification).

What are the approximate eigenvalues of the right shift operator $R$ on $\ell_\infty$

Rearrangement of Absolutely convergent series of series.

Trouble understanding definition of complex logarithm of Dirichlet L function.

If $X_n$ is an $L_1$-bounded martingale, show that $\sum_n(X_n-X_{n-1})^2< \infty$ a.s.

Clarification on a solution for Atiyah-Macdonald Chapter 1 Q.3.

Soft Question: Texts for introduction into Complex/Analytic Geometry i.e. GAGA theorems, Several Complex variables.

Explanation of Cardinal Arithmetic Used in Proving that bases of Vector spaces have the same cardinality.

Are free Artinian modules finitely generated?

Using Martingales to find expected values.

Show that integral operator of positive definite kernel is positive.