Dugundji Extenders
by
H.H. Hung
Concordia University

Given a monotonically normal^f, hereditarily paracompact T₁-space (X, \Cal T). Given a closed subspace Y. There is on \Cal C(Y) a linear extender \Phi into \Cal C(X) so that, for each f in \Cal C(Y), the range of \Phi(f) is contained in the convex hull of that of f, provided there is a shrinking A of open neighbourhoods on X such that

(*) given \xi in X \Y so that the collection \CalF_\xi \equiv {(y, V): y in  \textbdy  Y, y in V in \Cal T, \xi in A(y, V)} is non-void, there is [^(\xi)] in Y so that [^(\xi)] in W for any (z, W) in \Cal F_\xi.

^fWe do not need the full strength of monotone normality. We hardly need that of the Property B of 98T-54-04 (Abs. AMS 19 (1998) 218).

Date received: February 12, 1998