On continuous extension of uniformly continuous functions and metrics

T. Banakh, et al. "On continuous extension of uniformly continuous functions and metrics." Colloquium Mathematicae 116.2 (2009): 191-202. <http://eudml.org/doc/284328>.

@article{T2009,
abstract = {We prove that there exists a continuous regular, positive homogeneous extension operator for the family of all uniformly continuous bounded real-valued functions whose domains are closed subsets of a bounded metric space (X,d). In particular, this operator preserves Lipschitz functions. A similar result is obtained for partial metrics and ultrametrics.},
author = {T. Banakh, N. Brodskiy, I. Stasyuk, E. D. Tymchatyn},
journal = {Colloquium Mathematicae},
keywords = {extension operator; modulus function; continuity},
language = {eng},
number = {2},
pages = {191-202},
title = {On continuous extension of uniformly continuous functions and metrics},
url = {http://eudml.org/doc/284328},
volume = {116},
year = {2009},
}

TY - JOUR
AU - T. Banakh
AU - N. Brodskiy
AU - I. Stasyuk
AU - E. D. Tymchatyn
TI - On continuous extension of uniformly continuous functions and metrics
JO - Colloquium Mathematicae
PY - 2009
VL - 116
IS - 2
SP - 191
EP - 202
AB - We prove that there exists a continuous regular, positive homogeneous extension operator for the family of all uniformly continuous bounded real-valued functions whose domains are closed subsets of a bounded metric space (X,d). In particular, this operator preserves Lipschitz functions. A similar result is obtained for partial metrics and ultrametrics.
LA - eng
KW - extension operator; modulus function; continuity
UR - http://eudml.org/doc/284328
ER -