Linked Questions
65 questions linked to/from Examples of common false beliefs in mathematics
13
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2
answers
2k
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Math overdose? Professional advise how to cope with it [closed]
I'm a PhD student, currently working on my Thesis. Over the years I have many time encountered a problem. Maybe professional mathematicians know what I'm talking about?
When I study a math topic, ...
31
votes
3
answers
5k
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Is "compact implies sequentially compact" consistent with ZF?
Over at the nForum, we've been discussing sequential compactness. The discussion led me to realise that I naively assumed that nets were simply Big Sequences, and that I could make a reasonable guess ...
17
votes
1
answer
2k
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Uniformly integrable sequence such that a.s. limit and conditional expectation do not commute
Hi,
Could anyone give an example such that:
$$Y_i \rightarrow Y_{\infty}, \text{a.s.},$$
and $Y_i$'s are uniformly integrable.
But $\mathbb{E}(Y_i|\mathcal{G})$ does not converge a.s. to $\mathbb{E}(...
10
votes
1
answer
2k
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Set Theory and V=L
From http://en.wikipedia.org/wiki/Analytical_hierarchy
"If the axiom of constructibility holds then there is a subset of the product of the Baire space with itself which is $\Delta^1_2$ and is the ...
5
votes
3
answers
1k
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Non-continuous higher differentiability
The standard definition is that a function $f:\mathbb{R}^n\to \mathbb{R}$ is differentiable at a point $x$ if there exists a linear map $\mathrm{d}f_x: \mathbb{R}^n \to \mathbb{R}$ such that
$$f(x+h) ...
10
votes
2
answers
652
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Unconditionally convergent series in some functional spaces
Linked with this question and discussion
(Bilinear product of two summable families), I am very
interested in counterexamples/results about the following questions (cf the end).
First, I recall that a
...
2
votes
1
answer
2k
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Under which conditions: dim(W1 + W2 + W3) = dim(W1) + dim(W2) + dim(W3) − dim(W1 ∩ W2) − dim(W2 ∩ W3) − dim(W3 ∩ W1) + dim(W1 ∩ W2 ∩ W3) [closed]
Let $V$ be a finite dimensional vector space over a field $K$, and let $W_1$, $W_2$ and $W_3$ be subspaces of $V$. By analogy with the inclusion-exclusion principle for sets, and taking into account ...
11
votes
1
answer
726
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Is the category $\operatorname{sVect}$ an "algebraic closure" of $\operatorname{Vect}$?
$\DeclareMathOperator\sVect{sVect}\DeclareMathOperator\Vect{Vect}$The category $\sVect_k$ of (let's say finite-dimensional) super vector spaces can be obtained from the category $\Vect_k$ of (finite-...
4
votes
3
answers
1k
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Godel's Second Incompleteness theorem and Models
As I understand it, Godel's completeness theorem essentially says that if a sentence $\phi$ can be proven in a first order theory $\Gamma$, then $\phi$ is satisfied in all models $\mathcal{U}$ of $\...
8
votes
2
answers
569
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Attempted Banachification of a space
In a recent blog post, Terry Tao mentioned the question of how to tell if a Hausdorff topological vector space admits a finer topological structure which happens to be the topology of a Banach space (...
7
votes
2
answers
698
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$H^{*}$ algebras as a generalization of $C^{*}$ algebras
Let $H$ be the quaternions algebra. An $H^{*}$ algebra is a normed ring $A$ which is simultaneously a unital left $H$ module and has an involution $*$ with the following properties:
$\forall \lambda \...
7
votes
1
answer
2k
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Orthonormal bases on Reproducing Kernel Hilbert Spaces
Recall that a Hilbert space $\mathcal{H}$ is a reproducing kernel Hilbert space (RKHS) if the elements of $\mathcal{H}$ are functions on a certain set $X$ and for any $a\in X$, the linear functional $...
10
votes
1
answer
1k
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Are all quotients of a weakly contractible space via a free group action classifying spaces of the group?
I asked this question on math.stackexchange a week ago, but did not get an answer.
First of all, I don't want to restrict to any kind of "nice spaces" since I am interested in the most general ...
16
votes
1
answer
2k
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The homology of the orbit space
Suppose we have an acyclic group $G$ and let $X$ be a contractible CW-complex such that $G$ acts freely on $X$ (we do not suppose that the action is proper).
Is there a way to understand the homology ...
7
votes
1
answer
550
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Is there an integral fusion ring which is not of Frobenius type?
Combinatorially, a fusion ring $\mathcal{F}$ is nothing but a finite set $B=\{b_1, \dots, b_r\}$ (generating the $\mathbb{Z}$-module $\mathbb{Z} B$) together with fusion rules: $$ b_i \cdot b_j = \...