View : 31 Download: 0

A STUDY OF MULTIVALUE FUNCTIONS

Title
A STUDY OF MULTIVALUE FUNCTIONS
Authors
정계선
Issue Date
1983
Department/Major
대학원 수학과
Keywords
MULTIVALUEFUNCTIONS수학다가함수
Publisher
이화여자대학교 대학원
Degree
Master
Abstract
The properties of multivalued functions have been studied independently by several authors; Smithson [5], whyburn [9], Ponomarev [10, 11] and others. However the concepts and the theorems which they had presented have a slight differences. In this paper, we attempt to systemize these differences and give them a uniformized view thereafter. In particular, as a main theorem we obtain a generalized form of Urysohn's lemma concerning upper semi-continuous (or lower semi-continuous) function. Because a continuous multivalued function is a generalization of a continuous single-valued function, many of the results on continuous multivalued functions are generalized form of continuous single-valued functions. However, since upper semi-continuity (or lower semi-continuity) is a weakened form of continuity of single-valued function, it can be easily guessed that some stronger conditions other than normality will be required in order to satisfy the Urysohn's lemma. We show that stratifiability of a space satisfies the above necessity. The theorem is as follows : Let A and B be disjoint closed subsets of a stratifiable space X. Then there exists a USC-function F:X→[0, 1] such that F[A] = 0 and F[B] = 1.
Fulltext
Show the fulltext
Appears in Collections:
일반대학원 > 수학과 > Theses_Master
Files in This Item:
There are no files associated with this item.
Export
RIS (EndNote)
XLS (Excel)
XML


qrcode

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

BROWSE