Tagged Questions

0
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0answers
1 views

How do I find abelian subcategories of periodic triangulated categories?

If $T$ is a triangulated category, then the formalism of $t$-structures gives a way to find abelian subcategories inside. You're supposed to find two strictly full subcategories, …
29
votes
9answers
2k views

Why is Set, and not Rel, so ubiquitous in mathematics?

The concept of relation in the history of mathematics, either consciously or not, has always been important: think of order relations or equivalence relations. Why was there the n …
0
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0answers
20 views

Octonions and the Fano plane.

Does the Fano plane mnemonic for octonion multiplication have any deeper meaning? http://upload.wikimedia.org/wikipedia/commons/2/2d/FanoPlane.svg The symmetry group of the Fano …
2
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0answers
13 views

A duality on partial permutations

A partial permutation matrix $\pi$ is one with at most one 1 in any row and column (the rest 0s). Given one, we can cross out to the East and South (but not Southeast) of each 1. S …
5
votes
5answers
875 views

Groupoid actions on spaces

The action of a group $G$ on a topological space $X$ can be viewed as a functor $F: G \to \mathcal{Top}$ with $F(*)=X$. (Here I'm viewing a group as a category with one object, $ * …
1
vote
1answer
75 views

Set Theory exercise.

I find myself unable to solve question 24.1 of T. Jech's Set Theory: If $\beta<\omega_1$ and if $2^{\aleph_{\alpha}}\leq\aleph_{\alpha+\beta}$ for a stationary set of $\ …
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0answers
14 views

An integral with Gamma functions (Part 2)

I was wondering if there is a generalization of the integral discussed here to a case like, $\int \frac{d^dq}{q^{\nu_1}\vert \vec{q} \pm \vec{k}_1\vert ^{\nu_2}\vert \vec{q} \pm \ …
0
votes
0answers
31 views

DAG graph and topologic order question

I need to find the maximum number of topological sorts on Direct Acyclic Graph of N-order. I've checked by running Depth first search algorithm on various Direct Acyclic graphs, an …
2
votes
1answer
80 views

Is a Cauchy principal value invariant under a “change of variables”?

Let $f \in C^{\gamma}_c(\mathbb{R}) $. Let $K:\mathbb{R}^n \backslash {\vec{0}} \rightarrow \mathbb{R}^n$ be a singular integral kernel with the following properties: 1) K smooth …
4
votes
2answers
249 views

Importance of separability vs. second-countability

For me second-countability always felt like to be the more important and fundamental concept from general topology than separability. I wonder whether there are any points which ca …
0
votes
1answer
23 views

decomposition of the injective hull of a torsion free module

Let R be any ring and let A be a torsion free R-module. when would we be able to decompose the injective hull E(A) of A, i.e. when can we write E(A) as a sum E_i, i in I?
1
vote
1answer
95 views

exceptional divisor on a smooth surface

Let $D=\sum d_iD_i$ be an exceptional divisor on a smooth projective surface $X$. i.e., the intersection matrix $(D_i.D_j)$ is negative definite. I have 2 stupid questions. Fix …
14
votes
1answer
560 views

Under exactly what (extra) conditions (if any) is a connected Hausdorff manifold with a Riemannian metric a metric space?

The setting is that manifolds are Banach manifolds, not necessarily finite dimensional. No other assumption is made about the topology of the manifold. In particular, it is not ass …
0
votes
0answers
80 views

Strong convergence in the Bochner space L^p([0,T],X)

Dear mathoverflowers, I have a question concerning the strong convergence in $L^p([0,T],X)$. Let $X_1,X$ be two Banach spaces such that $X_1\subset X$ with compact embedding. Let …
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votes
2answers
121 views

Vector field pull back from embedding

Let $M$ and $N$ be finite dimensional smooth manifolds. A smooth map $f: M \to N$ is an embedding if and only if there is an open neighborhood $U$ of $f(M)$ in $N$ and a smooth ma …

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