Realcompactness and spaces of vector-valued functions

Jesus Araujo. "Realcompactness and spaces of vector-valued functions." Fundamenta Mathematicae 172.1 (2002): 27-40. <http://eudml.org/doc/283105>.

@article{JesusAraujo2002,
abstract = {It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y; in particular we find remarkable differences with respect to the scalar context: namely, if E and F are infinite-dimensional and T: C*(X,E) → C*(Y,F) is a biseparating map, then the realcompactifications of X and Y are homeomorphic.},
author = {Jesus Araujo},
journal = {Fundamenta Mathematicae},
keywords = {biseparating map; spaces of vector-valued functions; realcompactness; homeomorphic compactifications},
language = {eng},
number = {1},
pages = {27-40},
title = {Realcompactness and spaces of vector-valued functions},
url = {http://eudml.org/doc/283105},
volume = {172},
year = {2002},
}

TY - JOUR
AU - Jesus Araujo
TI - Realcompactness and spaces of vector-valued functions
JO - Fundamenta Mathematicae
PY - 2002
VL - 172
IS - 1
SP - 27
EP - 40
AB - It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y; in particular we find remarkable differences with respect to the scalar context: namely, if E and F are infinite-dimensional and T: C*(X,E) → C*(Y,F) is a biseparating map, then the realcompactifications of X and Y are homeomorphic.
LA - eng
KW - biseparating map; spaces of vector-valued functions; realcompactness; homeomorphic compactifications
UR - http://eudml.org/doc/283105
ER -