On contra continuous functions in topological spaces
Other Title(s)
حول الدوال المتصلة المضادة
Dissertant
al-Fayyumi, Hanadi Anwar Muhammad
Thesis advisor
Comitee Members
Asad, Asad Yusuf
Safi, Ziyad Rizq
University
Islamic University
Faculty
Faculty of Science
Department
Department of Mathematics
University Country
Palestine (Gaza Strip)
Degree
Master
Degree Date
2015
English Abstract
In this thesis, we study contra continuous functions in topological spaces.
We show that A function f : X ! Y is contra continuous i for each point x 2 X and each lter base in X convergent to x, the lter base f() is c-convergent to f(x).
Next, we introduce two independent classes of closed sets called tgr-closed sets and tgr-closed sets.
We show that the class of tgr-closed sets contains all dense sets and regular closed sets and is contained in the class of rg-closed sets and rwg-closed sets.
Also, we show that the class of tgr-closed sets contains all regular closed sets and is contained in the class of gr-closed sets and swg-closed sets.
We show that these two classes are the same in a locally indiscrete space.
Also, we study the topology generated by tgr-closed sets and show that the generated topology is contained in the space if and only if (X; ) is tgr-locally indiscrete.
Finally, we introduce and study new classes of contra continuous functions called contra tgr-continuous functions and contra tgr-closed sets.
Main Subjects
Topics
No. of Pages
76
Table of Contents
Table of contents.
Abstract.
Introduction.
Chapter One : Preliminaries.
Chapter Two : Contra continuous functions.
Chapter Three : New classes of generalized closed sets in topological spaces.
Chapter Four : New classes of contra continuous functions.
References.
American Psychological Association (APA)
al-Fayyumi, Hanadi Anwar Muhammad. (2015). On contra continuous functions in topological spaces. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-611026
Modern Language Association (MLA)
al-Fayyumi, Hanadi Anwar Muhammad. On contra continuous functions in topological spaces. (Master's theses Theses and Dissertations Master). Islamic University. (2015).
https://search.emarefa.net/detail/BIM-611026
American Medical Association (AMA)
al-Fayyumi, Hanadi Anwar Muhammad. (2015). On contra continuous functions in topological spaces. (Master's theses Theses and Dissertations Master). Islamic University, Palestine (Gaza Strip)
https://search.emarefa.net/detail/BIM-611026
Language
English
Data Type
Arab Theses
Record ID
BIM-611026