Comparative study of fuzzy topology

Dissertant

al-Diafi, Sahar Nawwaf Misbah

Thesis advisor

Mahdi, Hisham Bashir

Comitee Members

Asad, Asad Yusuf
Uqaylan, Muhammad Jamal

University

Islamic University

Faculty

Faculty of Science

Department

Department of Mathematics

University Country

Palestine (Gaza Strip)

Degree

Master

Degree Date

2014

English Abstract

-In this thesis, we will study Chang, Lowen and Sostak fuzzy topologies which are the most important and usefully between definitions of fuzzy topologies.

Then we give some functions which convert one of them to another or to the ordinary topology.

We study the fuzzy continuity, separations axioms and compactness, each of them have several definitions whith respect to what definition of fuzzy topology we use.

We give a comparative and preferring between them.

Both of Chang and Lowen define the fuzzy continuity.

We prefer the first one since it is parallel with the definition and theorems in the ordinary topology.

When we studied the separation axioms the main attention paid for T1-ness as an important properties, we give many definitions of T1-space and prefer some of them depending on the good extensions properity (i.e.

if the ordinary topology is T1-space then the extension fuzzy space is also fuzzy T1-space).

Then we redefine these T1 definitions to define fuzzy T1, strong T1 and weak T1-spaces.

Moreover many authors define the fuzzy compactness.

We compare between them especially Chang and Lowen definitions.

Finally we study Sostak structures which is a generalization to Chang definitions.

We completed and rewrite some proofs of many theorems.

Main Subjects

Mathematics

No. of Pages

76

Table of Contents

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Language

English

Data Type

Arab Theses

Record ID

BIM-533095