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Jhon Doe
  • Member for 5 years, 10 months
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10 votes
2 answers
4k views

Subset of totally bounded set is totally bounded.

8 votes
3 answers
959 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.

7 votes
2 answers
717 views

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

6 votes
4 answers
2k views

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

5 votes
2 answers
2k views

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

5 votes
1 answer
367 views

Prove that no ordinal is an element of itself

5 votes
2 answers
155 views

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

5 votes
3 answers
1k views

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

5 votes
1 answer
759 views

Addition of continuous functions over topological spaces is continuous.

5 votes
0 answers
62 views

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

5 votes
1 answer
216 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.

4 votes
1 answer
102 views

Independence of functions of independent random variables.

4 votes
2 answers
218 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).

4 votes
1 answer
177 views

Prime Ideal Properly Contained in principal Ideal.

4 votes
0 answers
599 views

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

3 votes
1 answer
911 views

Restriction of Continuous Functions is Continuous (Epsilon-Delta)

3 votes
1 answer
88 views

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

3 votes
1 answer
413 views

Pullback of pushforward $\sigma$-algebra

3 votes
1 answer
177 views

Extended real line is 2nd Countable (Clarification).

3 votes
1 answer
222 views

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

3 votes
0 answers
113 views

Rearrangement of Absolutely convergent series of series.

3 votes
1 answer
69 views

Elements in non-Abelian simple Groups.

3 votes
2 answers
182 views

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

2 votes
0 answers
56 views

Using Martingales to find expected values.

2 votes
1 answer
38 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.

2 votes
0 answers
31 views

Are free Artinian modules finitely generated?

2 votes
1 answer
121 views

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

2 votes
0 answers
102 views

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

2 votes
1 answer
54 views

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

2 votes
1 answer
37 views

Questions regarding Markov chains.

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