On contra continuous functions in topological spaces

Other Title(s)

حول الدوال المتصلة المضادة

Dissertant

al-Fayyumi, Hanadi Anwar Muhammad

Thesis advisor

al-Mabhuh, Ahmad Abd al-Rauf

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

Mathematics

Topics

• Mathematical models

No. of Pages

76

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-611026