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Realcompactness and spaces of vector-valued functions

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Araujo J.

Fundamenta Mathematicae

2002

tom 172

nr 1

27-40

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.

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1 Fundamenta Mathematicae

1 Araujo J.

1 2002

Wyniki wyszukiwania

Realcompactness and spaces of vector-valued functions