MA 406, General Topology - Spring 2024

Instructor  : Chandan Biswas

Office : 202 F, Mathematics Department 

Office Hours :   4:30 - 5:30 pm, Monday

Office Phone :   +91 2225767485

Email :   cbiswas@iitb.ac.in  (if you don't hear back within 48 hours please send a reminder)

Schedule : The class meets twice a week, Monday/Thursday, 5:30 - 6:55 pm.

Textbook : Topology (updated second edition) byJames Munkres. 

Although we will closely follow this book and most of the homework problems will be assigned from this book, lecture notes will be posted to this website. You are also encouraged to refer to the following other standard books as well.


M. A. Armstrong, Basic Topology, Springer (India), 2004.

K. D. Joshi, Introduction to General Topology, New Age International, 2000. 

J. L. Kelley, General Topology, Van Nostrand, 1955.

G. F. Simmons, Introduction to Topology and Modern Analysis, McGraw-Hill, 1963.


Syllabus : 

open sets, closed sets, neighbourhoods, bases, sub bases, limit points, closures, interiors, continuous functions, homeomorphisms. Examples of topological spaces: subspace topology, product topology, metric topology, order topology. Quotient Topology: Construction of cylinder, cone, Moebius band, torus, etc. Connectedness and Compactness: Connected spaces, Connected subspaces of the real line, Components and local connectedness, Compact spaces, Heine-Borel Theorem, Local -compactness. Separation Axioms: Hausdorff spaces, Regularity, Complete Regularity, Normality, Urysohn Lemma, Tychonoff embedding and Urysohn Metrization Theorem, Tietze Extension Theorem. Tychnoff Theorem, One-point Compactification.Complete metric spaces and function spaces, Characterization of compact metric spaces, equicontinuity, Ascoli-Arzela Theorem, Baire Category Theorem. Applications: space filling curve, nowhere differentiable continuous function. 


Optional Topics (if time permits) : Topological Groups and orbit spaces, Paracompactness and partition of unity, Stone-Cech Compactification, Fundamental group.

Course Policy 

You are encouraged to attend lectures regularly. You should try to read the book/class notes and do all the assignment problems. All the relevant class materials and announcements will be posted on the webpage. Please feel free to ask questions during the class and office hours. 

Please Note 

Grading : 

Homeworks : 


Lecture notes :


All of the material discussed in the following lecture notes are available in some guise in one of the above references.