Should physicists deal with the question of the reality of spacetime? It is argued that they should since this is a question about the dimensionality of the world and it is physics that should answer it. Almost a hundred years have passed since 1908 when Hermann Minkowski gave a fourdimensional formulation of special relativity according to which space and time are united into an inseparable fo...

Let k be a field of characteristic two. We prove that monic polynomial f∈k[X] degree n≥1 is the minimal/characteristic symmetric matrix with entries in if and only it not product pairwise distinct inseparable irreducible polynomials. In this case, we f minimal size n. also any element α∈kalg eigenvalue n or n+1, first case happening α separable.

We show that the Lipschitz structure of a separable quasi-Banach space does not determine, in general, its linear structure. Using the notion of the Arens-Eells p-space over a metric space for 0 < p ≤ 1 we construct examples of separable quasi-Banach spaces which are Lipschitz isomorphic but not linearly isomorphic.

We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. Then we prove that a separable reflexive Banach space with the unconditional tree property embeds into a reflexive Banach space with an unconditional basis. This solves several long standing open problems. In particular, it yields that a quotient...

a consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable hilbert space. it is proved, through a kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the hilbert space. as an application, this will naturally accomplish the work of kante...

We introduce a new consistency condition for neutral social welfare functions, called hyperstability. A social welfare function α selects a complete weak order from a profile PN of linear orders over any finite set of alternatives, given N individuals. Each linear order P in PN generates a linear order over orders of alternatives,called hyper-preference, by means of a preference extension. Henc...

In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional Banach space that is very different from—and considerably shorter than—the one recently given by Bermúdez, Bonilla and Martinón. We also show the existence of a strongly dense family of topologically mixing operators on every separable infinite...

If G is a Polish group, then the category of Polish G-spaces and continuous G-mappings has a universal object. §0. Preface It is known from [2] that 0.1. Theorem (de Vries). Let G be a separable locally compact metric group. Then the category of continuous G-maps and separable complete metric G-spaces has a universal object. In other words, there is a separable complete metric space X on which ...

We prove that a compact metric space (or more generally an analytic subset of a complete separable metric space) of Hausdorff dimension bigger than k can be always mapped onto a k-dimensional cube by a Lipschitz map. We also show that this does not hold for arbitrary separable metric spaces. As an application we essentially answer a question of Urbański by showing that the transfinite Hausdorff...