A simultaneous selection theorem

• Autorzy: Alexander D. Arvanitakis
• Języki publikacji: EN

Abstrakty

EN

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(𝓒,X) where 𝓒 denotes the Cantor set. For X = ℝ, this gives the well known Milyutin Theorem.

Kategorie tematyczne

• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 54C20: Extension of maps
• 54C65: Selections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 219
• Numer: 1
• Strony: 1-14

Daty

wydano

2012

Twórcy

autor

Alexander D. Arvanitakis

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

Identyfikatory

DOI

10.4064/fm219-1-1