Search Results

I am interested in the history of the proof of Artin's Theorem (on the diassociativity of alternative rings). Question. When has Artin proved this theorem and where was it published for the first tim …

I am looking for a reference to the bipartite version of the Schoenberg's criterion of embeddability into a Hilbert space. The Schoenberg criterion is formulated as Proposition 8.5(ii) of the book "G …

In the Wikipedia paper on Hadamard spaces, it is written that every flat Hadamard space is isometric to a closed convex subset of a Hilbert space. Looking through references provided by this Wikipedia …

At the moment I am writing a textbook in Foundations of Mathematics for students and trying to give a precise definition of a mathematical structure, which is the principal notion of structuralist app …

My question concerns the classical Desargues Theorem and its simplest version The small Desargues Theorem: Let $A$, $B$, $C$ be three distinct parallel lines and $a,a'\in A$, $b,b'\in B$, $c,c'\in C$ …

The picture below proves (without words) that it is possible to draw the classical Desargues configuration $D_{10}$ using points in the set $\{-3,-2,-1,0,1,2,3\}^2$. This picture was produced by Alex …

In fact, I asked this question hoping to find some appropriate name that can be legally used for naming affine spaces satisfying the small Desargues Theorem. Now I have learned that in Projective Geom …

I am looking for the reference to the following (surely known) characterization of metric spaces that embed into $\mathbb R^n$: Theorem. Let $n$ be positive integer number. A metric space $X$ is isom …

I am interested in the history related to algebraic numbers and have two questions: Who first proved that algebraic numbers form a field? Who first proved that algebraic numbers form an algebraicall …

For points $x,y,z$ of a metric space $(X,d)$ we write $\mathbf Mxyz$ and say that $y$ is a midpoint between $x$ and $z$ if $d(x,z)=d(x,y)+d(y,z)$ and $d(x,y)=d(y,z)$. Definition: A metric space $(X,d) …

By a Tarski space I understand a mathematical structure $(X,B,E)$ consisting of a set $X$, a ternary betweenness relation $B\subseteq X^3$ and a 4-ary equidistance relation $E\subseteq X^2\times X^2$ …

The answer to this question is negative. Consider the subspace $M_1=\{0\}\cup\{\frac 1n+\tfrac{i}{nm}:n,m\in\mathbb N\}$ of the complex plane and the space $M_2=M_1\cup\{\frac1n:n\in\mathbb N\}$ endow …

Definition. A semigroup $X$ is called $E$-separated if for any distinct idempotents $x,y\in X$ there exists a homomorphism $h:X\to Y$ to a semilattice $Y$ such that $h(x)\ne h(y)$. Observe that $X$ is …

I finally found an answer to my own question: by an old (nontrivial) result of Putcha and Weissglass, a semigroup $X$ is $E$-separated if and only if it is viable. A semigroup $X$ is viable if for any …

This is a very good (and also well studied) question, especially for homeomorphisms of measures. For example, the Haar measures on the zero-dimensional compact groups $\mathbb Z_2^\omega$ and $\mathbb …