Realcompactness and spaces of vector-valued functions
نویسنده
چکیده
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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تاریخ انتشار 2008