Realcompactness and spaces of vector-valued functions

• Autorzy: Jesus Araujo
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 54C40: Algebraic properties of function spaces
• 54C35: Function spaces
• 54D60: Realcompactness and realcompactification

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 172
• Numer: 1
• Strony: 27-40

Daty

wydano

2002

Twórcy

autor

Jesus Araujo

• Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, Avenida de los Castros s.n., E-39071 Santander, Spain

Identyfikatory

DOI

10.4064/fm172-1-3