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MathOverflow : Recent Questions and Answers (Page 31)

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Duality of finite signed measures and bounded continuous functions

Let $E$ be a metric space, $C_b(E)$ denote the space of bounded continuous functions $Etomathbb R$ (equipped with the supremum norm), $mathcal M(E)$ denote the space...

Asked on 02/02/2021

3 answer

Toposes with only preorders of points

For a Grothendieck topos $mathcal{E}$, are the following assertions equivalent? $(i)$ $mathcal{E}$ is localic.$(ii)$ The diagonal geometric morphism $mathcal{E} to mathcal{E} times mathcal{E}$ is...

Asked on 02/01/2021 by Matthias Hutzler

1 answer

Spanning trees: the last darn $1/4$

Let $Gamma$ be a connected graph. By (Kleitman-West, 1991),if every vertex of $Gamma$ has degree $geq 3$, then $Gamma$ has a spanningtree with ...

Asked on 01/31/2021 by H A Helfgott

1 answer

The level sets of a differentiable function is a manifold

I have seen stronger propositions that imply this, but both their statement and their proofs require more advanced tools than I'd like to use in my text, which is aimed...

Asked on 01/31/2021 by user8948

1 answer

Kruskal-Katona type question for union-closed families of sets

Question: Let $n,k$ be two positive integers with $n geq k$. Let $mathcal{F}$ be a family of $C(n,k)$ sets, each of size $k$, and let...

Asked on 01/30/2021 by Peter Hegarty

0 answer

First Chern class and field extensions

Let $X$ be a smooth, complex projective algebraic variety defined over a number field $K$.Let $D$ be a divisor of $X$ defined over $K$...

Asked on 01/28/2021 by manifold

1 answer

Distributive lattices with periodic Coxeter matrix

Let $L$ be a finite distributive lattice and $U$ its incidence matrix with entries $u_{i,j}=1$ iff $i leq j$ and $u_{i,j}=0$ else.Then $U^{-1}$...

Asked on 01/27/2021

0 answer

What does go wrong in Cellular homology if one considers projective limits of celullar complexes instead of CW-complexes?

Consider a nice topological space $X$ (e.g. the 3-sphere) and consider inside a decreasing sequence of compact subsets $(K_n)_{ninmathbb N}$ such that $K_infty:=bigcap_{nin mathbb N} K_n$...

Asked on 01/27/2021 by Léo Brunswic

0 answer

On $sum_{k=1}^nk^3 = x^3 + y^3$ with $x,y ge 1$

My question is related to https://oeis.org/A269839. It is well-known that there are parametric families of solutions for cubes that are sums of consecutive cubes: ...

Asked on 01/26/2021 by Alkan

0 answer

Is a set over which dynamics are topologically conjugate to a shift map on two symbols always repelling?

Consider the one-sided full shift map $sigma$ and the associated shift space of infinite sequences in two letters ${0,1}^mathbb{N}$ on which the shift map acts, equipped with the...

Asked on 01/26/2021 by aghostinthefigures

0 answer

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