TY - JOUR
T1 - Continuous linear extension of functions
AU - Koyama, A.
AU - Stasyuk, I.
AU - Tymchatyn, E. D.
AU - Zagorodnyuk, A.
PY - 2010/11
Y1 - 2010/11
N2 - Let (X, d) be a complete metric space. We prove that there is a continuous, linear, regular extension operator from the space C*b of all partial, continuous, real-valued, bounded functions with closed, bounded domains in X to the space C*(X) of all continuous, bounded, real-valued functions on X with the topology of uniform convergence on compact sets. This is a variant of a result of Kunzi and Shapiro for continuous functions with compact, variable domains.
AB - Let (X, d) be a complete metric space. We prove that there is a continuous, linear, regular extension operator from the space C*b of all partial, continuous, real-valued, bounded functions with closed, bounded domains in X to the space C*(X) of all continuous, bounded, real-valued functions on X with the topology of uniform convergence on compact sets. This is a variant of a result of Kunzi and Shapiro for continuous functions with compact, variable domains.
KW - Continuous linear operator
KW - Extension of functions
KW - Metric space
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U2 - 10.1090/S0002-9939-2010-10424-0
DO - 10.1090/S0002-9939-2010-10424-0
M3 - Article
AN - SCOPUS:78149233154
VL - 138
SP - 4149
EP - 4155
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 11
ER -