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-

On the computational properties of basic mathematical notions

“…Remark 4.42. Regarding item (iii), such functionals have been studied for about fifty years under the name simultaneous starting -it seems-with [56]. The notion of Caccioppoli set is also central to the Pfeffer integral, which is intermediate between the Lebesgue and gauge integral when restricted to the real line (see [7,75]).…”