Non-continuous set-valued functions

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Earl Dennett Fife (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Hughes Hoyle

Abstract: In [1] the concept of continuous set-valued functions is defined and developed. Somewhat continuous functions are defined in [2]. The purpose of this thesis is to extend the concept of somewhat continuity to set-valued functions and prove or disprove the natural extensions of theorems in [1] and [2]. In Chapter I, certain properties of functions which do not extend to set-valued functions are demonstrated, and their weakened extensions are proved. In Chapter II, the concept of a somewhat continuous set-valued function is defined in terms of upper semi-somewhat continuity and lower semi-somewhat continuity. The relationship between these types of set-valued functions and those which are upper semi-continuous and lower semi-continuous is investigated. In Chapter III, extensions and restrictions of upper semi-somewhat continuous and lower semi-somewhat continuous set-valued functions are investigated. In Chapter IV, the operation of composition on set-valued functions is defined. Conditions on functions to guarantee their composition is upper semi-somewhat continuous or lower semi-somewhat continuous are studied.

Additional Information

Language: English
Date: 1973
Set functions

Email this document to