Topology

Paper Code:

24DMAT812

Credits:

6

Contact Hours:

90.00

Max. Marks:

100.00

Objective:

This course will enable the students to

Understand the concept of fundamentals of point set topology.
Describe different topological spaces.
Aware about the need of the topology in mathematics.

Course Outcomes:

Learning

outcomes

(at course

level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

24DMAT

812

Topology

(Theory)

CO186: Analyze properties of topological spaces and construct various topologies on a general set.

CO187: Explain continuous functions, Homeomorphisms, Net and filters to understand structure of topological spaces.

CO188: Outline the concept of compactness and connectedness.

CO189: Categorize the separation axioms and produce examples for different topological spaces.

CO190: Explore the concept of product spaces and quotient spaces.

CO191: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Tutorials

Learning activities for the students:

Self learning assignments, Effective questions, Topic presentation, Assigned tasks

Quiz,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

Unit I:

Topological Spaces

18.00

Definition and examples, Closed sets, Neighborhood, Open base and sub base, Limit points, Adhere points and derived sets, Closure of a set.

Unit II:

Subspaces, Continuity and Nets and Filters

18.00

Subspaces, Continuity and homeomorphism, Nets, Filters and related theorems.

Unit III:

Compactness and Connectedness

18.00

Compact and locally compact spaces, Connected and locally connected spaces, Continuity and compactness, Continuity and connectedness.

Unit IV:

Separation axioms

18.00

T₀ space, T₁space, T₂ space of Hausdorff space, Regular and T₃ spaces, Normal and T₄ spaces.

Unit V:

Product spaces

18.00

Product space of two spaces, Product invariant properties for finite products, Quotient spaces.

Essential Readings:

George F. Simmons, Introduction to Topology and Modern Analysis, McGraw Hill, 2004.
Colin Adams and Robert Franzosa, Introduction to Topology, Pearsons united edition press, 2007.
K.D. Joshi, Introduction to General Topology, Wiley Eastern Ltd., 1985.
Dugundji. J, Topology, Prentice Hall of India, New Delhi, 1975.
Munkers R James, A first Course in Topology, Pearson Education Pvt. Ltd., Delhi, 2015.
Terry Lawson, Topology: A Geometric Approach, Oxford University press, 2003.

References:

· John L. Kelley, General Topology, Dover Publications; Reprint edition , 2017

· Stephen Willard, General Topology, Wesley Publishing Company, Reading, Massachusetts, 1970.

· Tej Bahadur Singh, Introduction to Topology, Springer Singapore, 2019.

· W.J. Pervn, Foundation of General Topology, Academic Press Ltd., 1996.

· M.G. Murdeshevar, Topology, Wiley Eastern Ltd, 1986.

e- RESOURCES

● https://qcpages.qc.cuny.edu/~jdodziuk/320-s2019/Seymour%20Lipschutz%20-%20Schaum's%20Outline%20of%20General%20Topology-McGraw-Hill%20(1968).pdf

● http://www.pdmi.ras.ru/~olegviro/topoman/eng-book-nopfs.pdf

● https://nptel.ac.in/courses/111106054

JOURNALS

● https://www.journals.elsevier.com/topology-and-its-applications