A simultaneous selection theorem
Volume 219 / 2012
Fundamenta Mathematicae 219 (2012), 1-14
MSC: Primary 54C65, 54C20; Secondary 46B03.
DOI: 10.4064/fm219-1-1
Abstract
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.
