A simultaneous selection theorem

Alexander D. Arvanitakis¹

¹ Department of Mathematics National Technical University of Athens 15780 Athens, Greece

Fundamenta Mathematicae, Tome 219 (2012) no. 1, pp. 1-14

Résumé

We prove a theorem that generalizes in a way both Michael's Selection Theorem and Dugundji's Simultaneous Extension Theorem. We use it to prove that if $K$ is an uncountable compact metric space and $X$ a Banach space, then $C(K, X)$ is isomorphic to $C(\mathcal{C}, X)$ where $\mathcal{C}$ denotes the Cantor set. For $X=\mathbb{R}$, this gives the well known Milyutin Theorem.

Détail

DOI : 10.4064/fm219-1-1

Keywords: prove theorem generalizes michaels selection theorem dugundjis simultaneous extension theorem prove uncountable compact metric space banach space isomorphic mathcal where mathcal denotes cantor set mathbb gives known milyutin theorem