# Thin-very tall compact scattered spaces which are hereditarily separable - Mathematics > Functional Analysis

Thin-very tall compact scattered spaces which are hereditarily separable - Mathematics > Functional Analysis - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We strengthen the property $\Delta$ of a function $f:\omega 2^2 ightarrow\omega 2^{\leq \omega}$ considered by Baumgartner and Shelah. This allows usto consider new types of amalgamations in the forcing used by Rabus, Juh\-aszand Soukup to construct thin-very tall compact scattered spaces. Weconsistently obtain spaces $K$ as above where $K^n$ is hereditarily separablefor each $n\in\N$. This serves as a counterexample concerning cardinalfunctions on compact spaces as well as having some applications in Banachspaces: the Banach space $CK$ is an Asplund space of density $\aleph 2$ whichhas no Fr\-echet smooth renorming, nor an uncountable biorthogonal system.

Autor: Christina Brech, Piotr Koszmider

Fuente: https://arxiv.org/