On the Extensions of Single Valued Continuous and Set Valued Usc Maps

Abstract

We show that two main theorems: (1) A regular space Y has a complete sequence if and only if the set valued usco map to Y defined on every dense set D of any space X has an usco extension over a G&#948;-set in X containing D. (2) A regular space Y with a G&#948;-diagonal has a complete sequence if and only if the single valued continuous map to Y defined on every dense set D of any space X has a continuous extension over a G&#948;-set in X containing D.</p