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QuantumSpace
  • Member for 3 years, 4 months
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17 votes

What does it mean for something to be strictly less than $\epsilon$ for an arbitrary $\epsilon$?

14 votes

How to understand what a 'noncommutative space' is

11 votes
Accepted

If $G$ is an abelian group, then inverse of $x$ is equal to $x$?

11 votes

Does there exists any non trivial linear metric space in which every open ball is not convex?

10 votes
Accepted

Is there a metric space such that every Cauchy sequence in it does not converge?

10 votes
Accepted

Do I miss something about a remark about topology in this lecture note?

9 votes
Accepted

How to find Isomorphism between groups of order 8

9 votes

Spivak Calculus. Why is the books proof valid? Is my attempt at a proof valid?

8 votes
Accepted

Why does $|A|\le|B|$ imply $|\mathcal{P}(A)|\le|\mathcal{P}(B)|$? (Use elementary notations; for beginners to advanced math)

8 votes
Accepted

John Conway's proof of Riesz representation theorem

7 votes
Accepted

Proof that $\mathbb{R}$ is not countable

7 votes
Accepted

In a metric space is a dense subset of a dense subspace dense in the space itself?

7 votes
Accepted

If a sequence is absolutely summable does this imply that the sum of the terms squared is finite.

7 votes

Why does dominated convergence theorem not apply when $f_{n}(x) =1$ for rational $x$ and $f_{n}(x) = 0$ otherwise?

7 votes

How to prove that a sequence is Cauchy

6 votes
Accepted

Let $T : V → V$ be linear. If $V$ is finite dimensional, show there's positive integer $k$ such that $T^{ k+1 }$and $T^ k$ have the same kernels.

6 votes
Accepted

$P_{n}(A)\xrightarrow{n \to \infty} P(A)$ for any $P$-continuity set $A$ iff $F_{n}(x)\xrightarrow{ n \to \infty} F(x)$ for all continuity points

6 votes
Accepted

Intuition for $\{X>0\}=\cup_{n\in\mathbb{N}}\{X\geq\frac1n\}$?

6 votes

If $n$ is the sum of two squares, then $n$ is not congruent to $3\pmod 4$

6 votes
Accepted

Why is $f(t) = e^{ta}$ differentiable in a unital Banach algebra?

6 votes

Is the map sends $T$ to $T^*$ adjoint of $T$ surjective?

5 votes
Accepted

knowing that $F(x)=\int^{x^3}_0\cos({t^2})dt$, how to disprove these statements?

5 votes

Rudin's definition of $L^1(\mu)$

5 votes

Let $f$ be continuous and positive

5 votes
Accepted

Uniqueness of C* norm and tensor product of C* algebra

5 votes
Accepted

Prove (or disprove) that a polynomial ring modulo an ideal is a field

5 votes

Proving isomorphic groups have the same number of subgroups.

5 votes

base for the topology

5 votes

Show that for all $\epsilon > 0$ the set $A_\epsilon = \{x \in X | d(x, A) < \epsilon\}$ is an open set in $X$

5 votes
Accepted

A locally compact and dense subset of a Hausdorff space is open

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