Course Details:

Review of metric spaces, Topological spaces, Continuous functions, Continuity by open sets, Metric topology, Subspace topology, Order topology, Product topology, Quotient topology, Surfaces as quotient spaces.

Compactness, Heine-Borel theorem, Sequential compactness, Limit point compactness, Locally compact spaces, Tychonoff’s theorem, Connectedness and path-connectedness, One-point Compactification.

Countability axioms, Separation axioms, Uryshon’s lemma and Tietze Extension Theorem.

Homotopic maps, Homotopy type, Fundamental group, Covering spaces, Fundamental group of the circle.

Text Books:

  1.  J. R.Munkres, Topology, Pearson Education India; 2 edition,2000
  2. M. A. Armstrong, Basic Topology, Undergraduate Texts in Mathematics, Springer-Verlag, 1983
  3. George Simmons, Introduction to Topology and Modern Analysis, McGraw Hill Education, 1963

Reference Books:

  1.  Allen Hatcher, Algebraic Topology, Cambridge University Press (2003)      
  2. T. W. Gamelin and  Robert E. Greene, Introduction to Topology, Dover Publications Inc (1999)
  3. I. M. Singer and J. A. Thorpe, Lecture notes on elementary topology and geometry, Springer-Verlag, New York-Heidelberg, 1976, 
  4. J P May. A Concise Course in Algebraic Topology, University of Chicago Press, 1999
  5. J Milnor. Topology from the Differentiable Viewpoint rev. ed., Princeton University Press, 1997
  6. V V Prasolov. Intuitive Topology, American Mathematical Society, 1995
  7. J R Weeks. The Shape of Space,. 2nd ed. CRC Press,  2002
  8. K D Joshi, Introduction to General Topology, 2nd Edition, New Age International Publishers