Main Page
About Science
Faculty Deanship
Letter of Dean
Overview of Deanship
Vice Deans
Vice Dean
Letter of Vice-dean
Overview of Vice-deanship
Vice Dean for Graduate Studies
Letter of Vice Dean for Graduate Studies
Overview of Vice Dean of Postgraduate Studies
Research and Innovation Unit
Vice Dean for Girls Campus
Faculty Management
Letter of Managing Director-Boys Campus
Letter of Managing Director-Girls Campus
Overview of Management
Educational Affairs
Males Campus
Staff
Females Campus
Contact Us
Research
عربي
English
About
Admission
Academic
Research and Innovations
University Life
E-Services
Search
Faculty of Sciences
Document Details
Document Type
:
Thesis
Document Title
:
On some gereralizations of continuity
حول بعض تعميمات الاتصال
Subject
:
Mathematics
Document Language
:
Arabic
Abstract
:
It is a well-known mathematical fact that the continuity of a function hinges on the supply of open sets. For instance, every function from a discrete space to an arbitrary space is continuous while no function from an indiscrete space to a non-indiscrete space is continuous. Realization of this simple truth led N. Levine to introduce the concept of a semi-open set in [1961, 1963]. Roughly speaking, a subset of a topological space is called semi-open if there exists an open set which is contained by this set while it is itself contained in the losure of the open set. Utilizing this generalization of open set to semi-open set enabled Levine to introduce semi- continuity etc. His work \vas followed by T. Hussain [1966], A. Singal and M. Singal [ 1968] and others. The primary aim of this work is to make a systematic study of various generalizations of continuity. We heavily rely upon the pioneering papers of N. Levine [1961], M. Singal and A. Singal [1968], and a series of papers by T. Noiri. . Chapter 1 is mainly devoted to the study of semi-open, pre-open and a-open sets. Using: Int and CI, various types of closures are defined and their interrelationships are investigated. In Chapter 2, a number of generalizations of continuity are introduced and their equivalences are studied. It is shown that if the topology on the ground set is appropriately varied, then two non-equivalent types of maps may become equivalent: Chapter 3. incorporates some latest developments in this field. An extensive study of the restrictions of various kinds of maps has been made to find out the hereditary characteristics of maps. Some closed graph theorems have been proved to show that the usual closed graph theorem remains valid for some generalizations of continuity. Lastly we have studied a remarkable generalization due to T. Noiri , [1990] of the result if t\VO continuous ma,ps agree on a dense subset of their domain, then they coincide on the whole domain
Supervisor
:
Prof. Mohammed Ali Al-Ghamdi
Thesis Type
:
Master Thesis
Publishing Year
:
1416 AH
1995 AD
Co-Supervisor
:
Dr. Bashir Ahmed Salimi
Added Date
:
Wednesday, June 11, 2008
Researchers
Researcher Name (Arabic)
Researcher Name (English)
Researcher Type
Dr Grade
Email
خديجة عبدالله شرف
Sharaf, Khadejah Abdullah
Researcher
Master
Files
File Name
Type
Description
23475.pdf
pdf
المستخلص
23476.pdf
pdf
Abstract
Back To Researches Page