Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, the set of all bounded continuous functions f: A → c, and 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 . 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-1-2,
author = {Kaori Yamazaki},
title = {Monotone extenders for bounded c-valued functions},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {17-22},
zbl = {1222.46007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-1-2}
}
Kaori Yamazaki. Monotone extenders for bounded c-valued functions. Studia Mathematica, Tome 196 (2010) pp. 17-22. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-1-2/