The present paper deals with a certain property of multivalued functions which coincides with the Darboux property in the case of single valued real functions of real variable. It is well known that derivatives, and hence approximately continuous functions have the Darboux property. The results contained here are generalizations of these properties to the multivalued case.
"On the Intermediate Value Property of Multivalued Functions." Real Anal. Exchange 26 (1) 245 - 260, 2000/2001.