A non-archimedean Dugundji extension theorem

Kąkol, Jerzy, Kubzdela, Albert, and Śliwa, Wiesƚaw. "A non-archimedean Dugundji extension theorem." Czechoslovak Mathematical Journal 63.1 (2013): 157-164. <http://eudml.org/doc/252476>.

@article{Kąkol2013,
abstract = {We prove a non-archimedean Dugundji extension theorem for the spaces $C^\{\ast \}(X,\mathbb \{K\})$ of continuous bounded functions on an ultranormal space $X$ with values in a non-archimedean non-trivially valued complete field $\mathbb \{K\}$. Assuming that $\mathbb \{K\}$ is discretely valued and $Y$ is a closed subspace of $X$ we show that there exists an isometric linear extender $T\colon C^\{\ast \}(Y,\mathbb \{K\})\rightarrow C^\{\ast \}(X,\mathbb \{K\})$ if $X$ is collectionwise normal or $Y$ is Lindelöf or $\mathbb \{K\}$ is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace $Y$ of an ultraregular space $X$ is a retract of $X$.},
author = {Kąkol, Jerzy, Kubzdela, Albert, Śliwa, Wiesƚaw},
journal = {Czechoslovak Mathematical Journal},
keywords = {Dugundji extension theorem; non-archimedean space; space of continuous functions; 0-dimensional space; Dugundji extension theorem; non-archimedean space; space of continuous functions; 0-dimensional space},
language = {eng},
number = {1},
pages = {157-164},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A non-archimedean Dugundji extension theorem},
url = {http://eudml.org/doc/252476},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Kąkol, Jerzy
AU - Kubzdela, Albert
AU - Śliwa, Wiesƚaw
TI - A non-archimedean Dugundji extension theorem
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 157
EP - 164
AB - We prove a non-archimedean Dugundji extension theorem for the spaces $C^{\ast }(X,\mathbb {K})$ of continuous bounded functions on an ultranormal space $X$ with values in a non-archimedean non-trivially valued complete field $\mathbb {K}$. Assuming that $\mathbb {K}$ is discretely valued and $Y$ is a closed subspace of $X$ we show that there exists an isometric linear extender $T\colon C^{\ast }(Y,\mathbb {K})\rightarrow C^{\ast }(X,\mathbb {K})$ if $X$ is collectionwise normal or $Y$ is Lindelöf or $\mathbb {K}$ is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace $Y$ of an ultraregular space $X$ is a retract of $X$.
LA - eng
KW - Dugundji extension theorem; non-archimedean space; space of continuous functions; 0-dimensional space; Dugundji extension theorem; non-archimedean space; space of continuous functions; 0-dimensional space
UR - http://eudml.org/doc/252476
ER -