Some kinds of strongly compact and pair-wise compact spaces

Dissertant

Nasir, Ahmad Ibrahim

Thesis advisor

Dawud, Narjis Abd al-Jabbar

University

University of Baghdad

Faculty

College of Education for Puresciences-IBN al-Haitham

Department

Department of Mathematics

University Country

Iraq

Degree

Master

Degree Date

2005

English Abstract

The main goal of our work is to create special types of compactness on a topological space (X, t) and on a bitopological space (X, ,), so we studied the concept of -compactness and defined for the first time (to the best of our knowledge) the concepts of semi -compactness and pre-compactness.

We proved new results (as we think) like; "The -continuous (Semi -continuous, pre-continuous", respectively) image of -compact (semi -compact, pre-compact space, respectively) is a compact space, with many corollaries, we give also many counter examples to show that semi -compact and pre-compact is stronger than that -compact, which is strongr than compact.

We add some conditions to get the opposite directions.

On the other hand, we give (to the best of our knowledge) new definitions of compactness in bitopologiocal spaces, namely N-compactness, pair-wise-semi--compactness and pair-wise pre-compactness, we have studied the properties of such spaces and the relationships among them and among other known types.

We also gave many counter examples to improve the ones which are invalid and put conditions to the invalid direction true.

Main Subjects

Mathematics

No. of Pages

109

Table of Contents

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Language

English

Data Type

Arab Theses

Record ID

BIM-742520