Course

M204 - Metric Spaces

Course No: 
M204
Credit: 
4
Prerequisites: 
M201
Approval: 
2014
UG-Core
Syllabus: 
Metric spaces, open balls and open sets, limit and cluster points, closed sets, dense sets, complete metric spaces, completion of a metric space, Continuity, uniform continuity, Banach contraction principle, Compactness, Connectedness, pathconnected sets. Sequences of functions, Pointwise convergence and uniform convergence, Arzela-Ascoli Theorem, Weierstrass Approximation Theorem, power series, radius of convergence, uniform convergence and Riemann integration, uniform convergence and differentiation, Stone Weierstrass theorem for compact metric spaces.
Text Books: 
  1. G. F. Simmons, “Introduction to Topology and Modern Analysis”, Tata McGraw-Hill, 2013.
  2. S. Kumaresan, “Topology of Metric Spaces”, Narosa Publishing House, 2005.
Reference Books: 
  1. R. R. Goldberg, “Methods of Real Analysis”, John Wiley & Sons, 1976.
  2. G. B. Folland, “Real Analysis”, Wiley-Interscience Publication, John Wiley & Sons, 1999.

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School of Mathematical Sciences

NISERPO- Bhimpur-PadanpurVia- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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