A note on the Dugundji extension theorem

Abstract

ABSTRACT.We prove that if A is a closed, metrizable, Gg-subspace of a collectionwise normal space X then there is a linear transformation e: C(A) -* C(X) such that for each g £ C(A), e(g) extends g and the range of e(g) is contained in the closed convex hull of the range of g. topology M on X having M C T.The second major ingredient in our proof is a slight generalization of the original Dugundji extension theorem wherein we consider pseudo-metriz-

Dugundji extension theorems for linearly ordered spaces

“…Example 3.3 shows that the assertion on page 806 of [10] that simultaneous extenders from C(A) to C(X) can be found provided A is a closed metrizable subspace of a paracompact space X is erroneous. The correct statement is that if A is a closed, metrizable, G^-subspace of the paracompact space X then simultaneous extenders from C(A) to C(X) exist [9].…”