GENERAL-5

General Topology

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by Dr. Mallikarjun Y. Kumbar,Prof. Narasimhamurthy S. K. ISBN Number : 978-1-73027-637-8

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Description

Dr. Mallikarjun Y. Kumbar(M.Sc., Ph.D.,)

Dr. Mallikarjun Y. Kumbar has 3 years of experience in

teaching Mathematics for different courses. He has taught

Mathematics for post graduate and under graduate courses. He

obtained the doctoral degree (Ph.D.,) under the guidance of

Prof. Narasimhamurthy S. K., in the year 2015. The title of his

thesis is “Finsler space and its applications to gravitational theory”. He obtained his

M.Sc. degree from the Kuvempu University with first class. He tries to keep himself

abreast of the development in the area of his interest in Finsler Manifold and

Relativity. He has published more than 12 papers in the prestigious international

journals. A couple of other papers have been communicated for publication. Also he

has attended and presented papers in more than 30 national/international

conferences/workshops.

Prof. Narasimhamurthy S. K.

Prof. Narasimhamurthy S. K., is a Chairman, Department of
P.G. studies and research in Mathematics, Kuvempu
University, Shimoga. He has 20 years of experience in
teaching Mathematics for different courses. He has taught
Mathematics for post graduate courses like M.Sc.,
M.Sc.,(Comp. Sc.,), MCA., etc. Beside he has proved to be an eminent researcher in
the area of his interest in Finsler Manifold and Relativity. He has guided 10 students
for their doctoral degree. Also awarded M.Phil.,degree for 12 students. He has
published more than 100 research papers in the prestigious international journals.
Also he has attended and gave invited talks in more than 80 national/international
conferences/workshops.

TOPOLOGICAL SPACES

1.1 De nition and examples

De nition 1.1. Let X be any non-empty set. A family = of subsets of X is

called a topology on X if it sati es the following conditions :

1.  2 = and X 2 =

2. A;B 2 = ) A B 2 =

3. A 2 =; 8 2 A (where A is any indexing set) )

S

2^

A 2 =

If = is a topology on X, then the ordered pair hX; =i is called a topological

space.

Example 1. Throughout X denotes a non-empty set.

1. = = f;Xg is a topology on X. This topology is called indiscrete topol-

ogy on X and the topological space hX; =i is called indiscrete topological

space.

1

Additional information

Weight 1.1 kg
Dimensions 1.1 cm

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