A simultaneous selection theorem

作者：Arvanitakis Alexander D^*

来源：Fundamenta Mathematicae, 2012, 219(1): 1-14.

DOI：10.4064/fm219-1-1

• selection theorem
• extension theorem

We prove a theorem that generalizes in a way both Michael%26apos;s Selection Theorem and Dugundji%26apos;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(C, X) where C denotes the Cantor set. For X = R, this gives the well known Milyutin Theorem.

• 出版日期2012