关于上半连续集值映象的连续选择问题

On the Problem of Continuous Selections for Upper Semicontinuous Maps

本文进一步研究了上半连续集值映象的连续选择问题．首先，用一反例指出Ａｕｂｉｎ Ｊ、 Ｐ［１］中一结果不能成立．另外，对上半连续映象的σ－可选择性给出了另一逼近形式的结果．

The purpose of this paper is to give a further study on the existence of continuous selections for upper semicontinuous multivalued maps. First we show that a statement in Aubin J. P.[1] about continuous selections is not correct by a counter example. Next we obtain some results with uniform approximation about selectionable properties of upper semicontinuous maps.