TOPOLOGY
- Understand the concept of fundamentals of point set topology.
- Understand the introduction to topological spaces.
- Aware about the need of the topology in Mathematics.
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Learning Outcomes |
Learning and teaching strategies |
Assessment |
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After the completion of the course the students will be able to: CLO31- Analyze properties of topological spaces and construct various topologies on a general set. CLO32 Apply the topological concepts and constructions to some chosen real world problems. CLO33 - Correlate the concept of continuity to compact and connected spaces. CLO34- - Categorize the separation axioms and produce examples for different topological spaces. CLO35- Understand the concept of product spaces and quotient spaces.
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Approach in teaching: Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstration, Team teaching Learning activities for the students: Self learning assignments, Effective questions, Simulation, Seminar presentation, Giving tasks, Field practical
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Presentations by Individual Student Class Tests at Periodic Intervals. Written assignment(s) Semester End Examination |
Topological Spaces: Definition and examples, Closed sets, Neighborhood, Open base and sub base, Limit points, Adhere points and derived sets, Closure of a set.
Subspaces, Continuity and homeomorphism, Nets, Filters.
Compact and locally compact spaces Connected and locally connected spaces, Continuity and compactness, Continuity and connectedness.
Separation axioms: T0 space, T1 space, T2 space or Hausdroff space, Regular and T3 spaces, Normal and T4 spaces.
Product spaces: Product space of two spaces, Product invariant properties for finite products, Quotient spaces.
- George F. Simmons, Introduction to Topology and ModernAnalysis, McGraw Hill , 2004.
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Colin Adams, Robert Franzosa, Introduction to Topology, Pearsons united edition press, 2007.
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K.D.Joshi, Introduction to General Topology, Wiley Eastern Ltd.,1983.
- 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.
- 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,1983.
