**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:**

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

**Reference Books:**

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