MathOverflow

I am trying to understand whether the following construction belongs to a standard model-theoretic or categorical framework. I posted a similar question on MathStackExchange.https://math.stackexchange.com/questions/5144148/how-should-this-descent-construction...

Suppose I am minimizing the Euclidean distance in $\mathbb{R}^{n}$ between a point $y$ and compact convex set $U$ (where $y\notin U$):
$\min_{x\in U}\|x-y\|$.
I believe the minimizer $x_{U}^{*}$ is unique and my question is about the continuity properties of the argmin mapping with respect to the choice of set $U$. That is, if I have two minimization problems, one with minimizing over set $U$ and one with...

For every $n\in \mathbb{N}$ Dente by $GDS(n)$ the space of all invertible $n\times n$ matrices which are double stochastic matrix. Is it really a Lie subgroup of $Gl(n,\mathbb{R})$ which is introduced in classic text books as a classical example of Lie...

For the first $N$ non-trivial zeros of $\zeta(s)$, consider
$$A(\tau; N) = \sum_{n=1}^{N} \exp(-i \tau \gamma_n)$$
where $\gamma_n$ is the imaginary part of the $n$-th zero. At frequencies$\tau = \log p$ for primes $p$, I observe that $\arg(A(\log p; N))$concentrates near $\pi$ (i.e. $A$ aligns with the negative real axis),already for $N$ as small as a few hundred...