Vol. 79, No. 2, 1978

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ISSN: 0030-8730
Multifunctions and graphs

James E. Joseph

Vol. 79 (1978), No. 2, 509–529
Abstract

In this paper we introduce the notions of multifunctions with strongly-closed graphs and 𝜃-closed graphs. We then extend these notions as well as the notion of multifunctions with closed graphs and use these extensions to generalize and extend various known results on multifunctions. These generalizations and extensions include a number of sufficient conditions for multifunctions to be upper-semi-continuous, several generalizations and extensions of the well-known Uniform Boundedness Principle from analysis, and several “fixed set” theorems.

Mathematical Subject Classification 2000
Primary: 54C60
Milestones
Received: 25 May 1977
Published: 1 December 1978
Authors
James E. Joseph