Course Details:

  1. Definition of Topological spaces, examples of topological spaces such as metric spaces, Continuous functions, Subspace topology, Product topology, Quotient topology. (11 Lectures)
  2. Compactness, Locally compact spaces, Tychonoff’s theorem, Compactifications. (6 Lectures)
  3. Connectedness and path-connectedness. (6 Lectures)
  4. Countability axioms, Separation axioms, Uryshon’s lemma and Tietze Extension Theorem. (13 Lectures)
  5. Metrizability, topologies on function spaces. (6 Lectures)

 

Learning Outcomes: At the end of the course the students should be able to:

 

  1. Create new topological spaces by using subspace, product and quotient topologies. 
  2. Use continuous functions and homeomorphisms to understand the structure of topological spaces. 
  3. State and prove standard results regarding various topological concepts, and decide whether statements about them are true, providing a proof or counterexample as appropriate.
  4. By the end of the course, a student should be able to understand and construct abstract arguments about topological spaces. 

Text Books

  1. J. R.Munkres, Topology, Pearson Education India; 2 edition (2000), ISBN-10: 9789332549531,  ISBN-13: 978-9332549531
  2. M. A. Armstrong, Basic Topology, Undergraduate Texts in Mathematics, Springer-Verlag, 1983, ISBN-10: 0387908390, ISBN-13: 978-03879083

References :

  1. T. W. Gamelin and  Robert E. Greene, Introduction to Topology, Dover Publications Inc (1999), ISBN-10: 0486406806, ISBN-13: 978-0486406800
  2. I. M. Singer and J. A. Thorpe, Lecture notes on elementary topology and geometry, Springer-Verlag, New York-Heidelberg, 1976, Reprint of the 1967 edition, Undergraduate Texts in Mathematics, ISBN-10: 1461573491, ISBN-13: 978-1461573494
  3. J Milnor. Topology from the Differentiable Viewpoint rev. ed., Princeton University Press, 1997, ISBN-10: 0691048339, ISBN-13: 978-0691048338
  4. V V Prasolov. Intuitive Topology, American Mathematical Society, 1995, ISBN-10: 0821803565, ISBN-13: 978-0821803561
  5. J R Weeks. The Shape of Space,. 2nd ed. CRC Press,  2002, ISBN-10: 0824707095, ISBN-13: 978-082470709
  6. K D Joshi, Introduction to General Topology, 2nd Edition, New Age International Publishers, ISBN-13: 978-8122436037