# A simultaneous selection theorem

Fundamenta Mathematicae (2012)

- Volume: 219, Issue: 1, page 1-14
- ISSN: 0016-2736

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topAlexander 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 -

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