Geodesic
Realcompactness and spaces of vector-valued functions
Jesus Araujo1
1 Departamento de Matemáticas, Estadística y Computación Facultad de Ciencias Universidad de Cantabria Avenida de los Castros s.n. E-39071 Santander, Spain
Fundamenta Mathematicae, Tome 172 (2002) no. 1, pp. 27-40

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $T: C^{*} (X,E) \rightarrow C^{*} (Y, F)$ is a biseparating map, then the realcompactifications of $X$ and $Y$ are homeomorphic.
DOI : 10.4064/fm172-1-3
Keywords: shown existence biseparating map between large class spaces vector valued continuous functions implies compactifications homeomorphic cases conditions given warrant existence homeomorphism between realcompactifications particular remarkable differences respect scalar context namely infinite dimensional * rightarrow * biseparating map realcompactifications homeomorphic

Jesus Araujo 1

1 Departamento de Matemáticas, Estadística y Computación Facultad de Ciencias Universidad de Cantabria Avenida de los Castros s.n. E-39071 Santander, Spain 
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Jesus Araujo. Realcompactness and spaces of vector-valued functions. Fundamenta Mathematicae, Tome 172 (2002) no. 1, pp. 27-40. doi: 10.4064/fm172-1-3

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