The main purpose of this work is to study the metrizability of the space of R-places of a function field, with transcendence degree 1 over a real closed field. Specifically, we are going to present a necessary and sufficient ...

The set of invariant probability measures of a continuous action of an amenable group on a compact metric space is a (non empty) metrizable Choquet simplex. A natural question is to know if the converse is true, i.e, if ...

Las líneas de investigación de esta propuesta tienen una unidad de origen y de objetivos. El análisis armónico en estructuras generales, es nuestra especialidad desde hace décadas. El problema general de la búsqueda de ...

We investigate the geometry of C(K, X) and ℓ ∞ (X) spaces through complemented subspaces of the form ( i∈Γ X i ) c 0 . For Banach spaces X and Y , we prove that if ℓ ∞ (X) has a complemented subspace isomorphic to c 0 (Y ...

We study Lipschitz-free spaces over compact and uniformly discrete metric spaces enjoying certain high regularity properties - having group structure with left-invariant metric. Using methods of harmonic analysis we show ...

A well-known consequence of the ergodic decomposition theorem is that the space of invariant probability Measures of a topological dynamical system, endowed with the weak* topology, is a non-empty metrizable Choquet simplex. ...

Norm Hilbert spaces (NHS) are defined as Banach spaces over valued fields (see 1.4) for which each closed subspace has a norm-orthogonal complement. For fields with a rank I valuation, these spaces were characterized already ...

In this paper we define sizable spaces and some related notions. We study their properties and their relations with other topological spaces. We discuss some metrization theorems and present several examples relevant ot ...