Monotone extenders for bounded c-valued functions

Kaori Yamazaki. "Monotone extenders for bounded c-valued functions." Studia Mathematica 199.1 (2010): 17-22. <http://eudml.org/doc/285622>.

@article{KaoriYamazaki2010,
abstract = {Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, $C_\{∞\}(A,c)$ the set of all bounded continuous functions f: A → c, and $C_\{A\}(X,c)$ the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender $u: C_\{∞\}(A,c) → C_\{A\}(X,c)$. This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer to a question posed by I. Banakh, T. Banakh and K. Yamazaki.},
author = {Kaori Yamazaki},
journal = {Studia Mathematica},
keywords = {monotone extender; Banach space ; strong Choquet; GO space; Michael line},
language = {eng},
number = {1},
pages = {17-22},
title = {Monotone extenders for bounded c-valued functions},
url = {http://eudml.org/doc/285622},
volume = {199},
year = {2010},
}

TY - JOUR
AU - Kaori Yamazaki
TI - Monotone extenders for bounded c-valued functions
JO - Studia Mathematica
PY - 2010
VL - 199
IS - 1
SP - 17
EP - 22
AB - Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, $C_{∞}(A,c)$ the set of all bounded continuous functions f: A → c, and $C_{A}(X,c)$ the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender $u: C_{∞}(A,c) → C_{A}(X,c)$. This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer to a question posed by I. Banakh, T. Banakh and K. Yamazaki.
LA - eng
KW - monotone extender; Banach space ; strong Choquet; GO space; Michael line
UR - http://eudml.org/doc/285622
ER -