User Jhon Doe

10 votes

2 answers

3k views

Subset of totally bounded set is totally bounded.

general-topology elementary-set-theory

asked Feb 26, 2018 at 3:27

8 votes

3 answers

951 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

712 views

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

ring-theory commutative-algebra maximal-and-prime-ideals

asked Mar 3, 2018 at 4:03

6 votes

4 answers

2k views

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

linear-algebra set-theory

asked Feb 12, 2017 at 14:13

5 votes

2 answers

2k views

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

linear-algebra elementary-set-theory

asked Feb 12, 2017 at 3:36

5 votes

1 answer

361 views

Prove that no ordinal is an element of itself

set-theory ordinals well-orders

asked Nov 6, 2017 at 0:03

5 votes

2 answers

153 views

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

abstract-algebra maximal-and-prime-ideals ring-homomorphism

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 $F$?

abstract-algebra proof-verification galois-extensions

asked Oct 1, 2018 at 9:09

5 votes

1 answer

741 views

Addition of continuous functions over topological spaces is continuous.

general-topology proof-verification continuity

asked Apr 16, 2019 at 14:22

5 votes

0 answers

62 views

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

real-analysis integration riemann-integration

asked Aug 30, 2020 at 9:03

5 votes

1 answer

213 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.

probability-theory measure-theory conditional-probability martingales

asked Feb 23, 2021 at 11:13

4 votes

1 answer

100 views

Independence of functions of independent random variables.

probability-theory measure-theory conditional-probability

asked Feb 24, 2021 at 4:01

4 votes

2 answers

217 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).

galois-theory roots

asked Oct 15, 2018 at 11:06

4 votes

1 answer

175 views

Prime Ideal Properly Contained in principal Ideal.

abstract-algebra ring-theory maximal-and-prime-ideals

asked May 3, 2018 at 9:54

4 votes

0 answers

589 views

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

real-analysis sequences-and-series uniform-convergence cauchy-sequences

asked Oct 27, 2017 at 17:36

3 votes

1 answer

906 views

Restriction of Continuous Functions is Continuous (Epsilon-Delta)

calculus real-analysis functions

asked Oct 23, 2017 at 13:18

3 votes

1 answer

88 views

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

sequences-and-series derivatives power-series limsup-and-liminf

asked Aug 16, 2018 at 0:31

3 votes

1 answer

404 views

Pullback of pushforward $\sigma$-algebra

measure-theory

asked Aug 22, 2019 at 12:50

3 votes

1 answer

174 views

Extended real line is 2nd Countable (Clarification).

general-topology

asked Aug 29, 2019 at 15:06

3 votes

1 answer

218 views

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

functional-analysis operator-theory spectral-theory

asked Mar 18, 2019 at 11:09

3 votes

0 answers

110 views

Rearrangement of Absolutely convergent series of series.

sequences-and-series absolute-convergence

asked Oct 16, 2019 at 5:12

3 votes

1 answer

69 views

Elements in non-Abelian simple Groups.

group-theory simple-groups

asked Aug 15, 2019 at 2:19

3 votes

2 answers

179 views

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

probability-theory measure-theory conditional-probability martingales

asked Feb 25, 2021 at 7:33

2 votes

0 answers

56 views

Using Martingales to find expected values.

probability-theory measure-theory conditional-probability martingales

asked Feb 24, 2021 at 19:08

2 votes

1 answer

37 views

Suppose $A$ is Artinian and commutative with 1. If $J(A)M=M$, then $M=\{0\}$. $J(A)$ is the Jacobson radical of A.

abstract-algebra modules

asked Jul 11, 2020 at 19:57

2 votes

0 answers

31 views

Are free Artinian modules finitely generated?

vector-spaces modules solution-verification free-modules

asked Jul 5, 2020 at 15:43

2 votes

1 answer

117 views

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

abstract-algebra algebraic-geometry soft-question manifolds several-complex-variables

asked May 9, 2020 at 7:50

2 votes

0 answers

101 views

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

abstract-algebra multivariate-polynomial

asked May 27, 2020 at 16:00

2 votes

1 answer

54 views

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

linear-algebra elementary-set-theory vector-spaces cardinals

asked Jun 14, 2020 at 15:44

2 votes

1 answer

37 views

Questions regarding Markov chains.

probability-theory measure-theory markov-chains conditional-probability conditional-expectation

asked Oct 5, 2021 at 14:57

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200 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.

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).

Prime Ideal Properly Contained in principal Ideal.

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 $

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.

Elements in non-Abelian simple Groups.

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

Using Martingales to find expected values.

Suppose $A$ is Artinian and commutative with 1. If $J(A)M=M$, then $M=\{0\}$. $J(A)$ is the Jacobson radical of A.

Are free Artinian modules finitely generated?

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

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

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

Questions regarding Markov chains.