A simultaneous selection theorem

Alexander D. Arvanitakis. "A simultaneous selection theorem." Fundamenta Mathematicae 219.1 (2012): 1-14. <http://eudml.org/doc/282856>.

@article{AlexanderD2012,
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(𝓒,X) where 𝓒 denotes the Cantor set. For X = ℝ, this gives the well known Milyutin Theorem.},
author = {Alexander D. Arvanitakis},
journal = {Fundamenta Mathematicae},
keywords = {selection theorem; extension theorem},
language = {eng},
number = {1},
pages = {1-14},
title = {A simultaneous selection theorem},
url = {http://eudml.org/doc/282856},
volume = {219},
year = {2012},
}

TY - JOUR
AU - Alexander D. Arvanitakis
TI - A simultaneous selection theorem
JO - Fundamenta Mathematicae
PY - 2012
VL - 219
IS - 1
SP - 1
EP - 14
AB - 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.
LA - eng
KW - selection theorem; extension theorem
UR - http://eudml.org/doc/282856
ER -