Monotone extensions of continuous functions
by
Phillip Zenor
Auburn University

If H is a closed subset of X, then e\colon C(H) --> C(X) is a monotone extender if

1. ef is an extension of f for every f in C(H) and

2. f(x) >= g(x) for all x in H implies that ef(x) >= eg(x) for all x in X.

We characterize those closed subsets of a monotonically normal space that admit monotone extenders.

Date received: February 22, 2003