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Realcompactness and spaces of vector-valued functions

Jesus Araujo
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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 is a biseparating map between the space of E-valued bounded continuous functions on X and that of F-valued bounded continuous functions on Y, then the realcompactifications of X and Y are homeomorphic.

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Jesus Araujo. 2001-05-14. Realcompactness and spaces of vector-valued functions. https://arxiv.org/abs/math/0010261

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