Maths Heading

ON ALMOST STRONG – I*S – OPEN SETS & DECOMPOSITION OF CONTINUITY VIA IDEALS A dissertation submitted to the Bharathiar University in partial fulfillment of the requirements for the award of the Degree of Master of Philosophy in Mathematics.

Submitted by A.A. NITHYA Reg.No. 2008R077

DEPARTMENT OF MATHEMATICS

NIRMALA COLLEGE FOR WOMEN (AUTONOMOUS) ACCREDITED WITH ‘ A’ GRADE BY NAAC Red Fields, Coimbatore – 18.

SEPTEMBER - 2009

Declaration

DECLARATION

I Mrs. A.A. NITHYA, here by declare that the dissertation, entitled, “ON ALMOST STRONG – I*S OPEN SETS AND DECOMPOSITION OF CONTINUITY VIA IDEALS” submitted to Bharathiar University in partial fulfillment of the requirements for the award of the Degree of Master of Philosophy in Mathematics is a record of original research work done by me during the period 2008-2009 under the supervision and guidance of Mrs. S. PONNUTHAI SELVARANI, M.Sc., M.Phil., Lecturer (SG), Head of the Department of Mathematics and it has not formed the basis for the award of any Degree / Diploma/Associateship/Fellowship or other similar title to any candidate of any university. Signature of the candidate

(A.A. NITHYA) Reg.No.2008R077

Certificate

CERTIFICATE

This is to certify that the dissertation, entitled, “ ON ALMOST STRONG – I*S – OPEN SETS AND DECOMPOSITION OF CONTINUITY VIA IDEALS” submitted to Bharathiar University in partial fulfillment of the requirements for the award of the Degree of Master of Philosophy in Mathematics is a record of original research work done by Mrs. A.A. NITHYA during the period 2008-2009 of her study in the Department of Mathematics at Nirmala College for Women, Coimbatore – 18, under my supervision and guidance and the dissertation has

not

formed

the

basis

for

the

award

of

any

Degree/Diploma/Associateship/Fellowship or other similar title to any candidate of any university.

Signature of the Guide

Mrs. S. PONNUTHAI SELVARANI M.Sc.,M.Phil., Lecturer (SG) Counter signed

Principal/Head of the Department

ACKNOWLEDGEMENT I wish to express my deep sense of gratitude and thanks to my guide Mrs. S. PONNUTHAI SELVARANI M.Sc., M.Phil., Lecturer (SG) and Head of

the Department of Mathematics for her valuable

guidance and the untiring interest in the preparation of this work. Words cannot express her persistent effort and affectionate endeavors to create love for the subject and logical thinking. I express my sincere thanks to Rev. Sr. PAULINE MARY, M.Sc. ,M.Phil., Principal, Nirmala College for Women, Coimbatore, for providing all the necessary facilities to carry on the dissertation successfully. I am very much greatful to Dr. Sr. I. AROKIA RANI, Reader, Department of Mathematics for her guidance in completion of this project work. I extend my deep sense of gratitude to all members of the department for their valuable suggestions and encouragement during my project work. I equally thank my beloved parents for their continuous support through out my project work. Above all I thank GOD ALMIGHTY for his endless blessings.

ABSTRACT In this dissertation, the new concepts namely, weakly semi - I*S - open set, almost I*Sopen sets, αI*S open sets, α-I*S continuous functions, are defined and studied. Completely codense ideals are defined and characterized in terms of weakly semi-I-open sets. Weakly semi -I*S-continuous functions are introduced

to

obtain

a

decomposition

of

continuity. The fundamental properties of such functions are also investigated.

Acknowledgement

CONTENTS

CHAPTER –I

CHAPTER –II

ABSTRACT

BIBLIOGRAPHY