Some complemented function spaces in c(x)

Abstract

Et X and Z be compact Hausdorff spaces, and let P be a linear subspace of C(X) which is isometrically isomorphic to C(Z). In this paper conditions, some necessary and some sufficient, are presented which insure that P is complemented in C(X). For example if Xis metrizable, P contains a strictly positive function, and the decomposition induced on X by P is lower semi-continuous then P is complemented in C(X). © 1968 by Pacific Journal of Mathematics.