# All Questions

98,519 questions
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### Regularity of John's ellipsoid

Consider a finite dimensional real Banach space $E$, with norm say $|\cdot|$. Let $N$ denote the set of all norms on $E$. Suppose that $\varphi_1, \varphi_2 \in N$ have unit balls $B_1$ and $B_2$, ...
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### Linear transformation group of paraboloid in $\mathbb{R}^d.$

Suppose $P$ is a paraboloid in $\mathbb{R}^d.$ What is the group of all linear transformations $\mathcal{L}: \mathbb{R}^d \rightarrow \mathbb{R}^d$ such that $\mathcal{L}(P)=P?$ Could someone please ...
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### A strong plus-one hypothesis

To make this more easily readable, I'll start with the question and then give the explanation/motivation. Question. Is the following principle (or its weakening, with "for every real $r$" replaced ...
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### Henselianizations over countable index sets

Let $A$ be a ring, $I\subset A$ a finitely generated ideal. The henselianization $A^h$ of $A$ along $I$ is the universal $A$-algebra that is henselian along $I$ and can be presented as a direct limit ...
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### Ramified covering morphisms

I found the following theorem in the book Revêtements Étales et Groupe Fondamental$-$Alexander Grothendieck. Théorème 10.11. — Soit $f : X\longrightarrow Y$ un morphisme quasi-fini séparé. On ...
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### Topological amenability vs amenability of an action

Let $G$ be a discrete group and let $X$ be a compact, Hausdorff space. Assume that $G$ acts on $X$ by homeomorphisms. Consider the following two definitions: [$C^*$-algebras and finite dimensional ...