Instructor : Chandan Biswas
Office : 202 F, Mathematics Department
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 each week, Tuesday/Friday, 5:30 - 6:55 pm.
Office Hours : Tuesday 4:30 - 5:30 pm.
TAs :
Bittu Singh
Email : 22d0781@iitb.ac.in
Office address : RS208, Mathematics Department
Office hour : Friday, 3 pm - 4pm
Sumanta Das
Email : 20004138@iitb.ac.in
Office address : B1 (Basement), Mathematics Department
Office hour : Monday, 10:00 – 11:00 AM
Textbook : Topology (updated second edition) byJames Munkres.
Although we will closely follow this book, 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 of the 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
Tutorials will be used to discuss the problems and any other questions that you may have. You are encouraged to attend these.
A pink slip is a must if asking for a make up exam.
No calculators are allowed in the exams.
Grading :
Quizzes : 40%
Midterm : 20%
Final exam : 40%.
List of problems :