Course Name: An introduction to Point-Set-Topology Part-I

Course abstract

The course will start with definition of metric spaces and topological spaces and proceeds to study topological aspects of metric spaces. W e prove three very important theorems on complete metric spaces and give construction of completion of metric spaces. The course then takes up the study of topological spaces, constructing new topologies from the old. Bases and subbases, I and II countability, separability, connected and path connectedness, Compactness , Lindeloffness, separation axioms etc. The course ends with the celebrated results such as Urysohn’s lemma and Titze’s extension theorem and some applications. The content of this course is mandatory for any meaningful study of analysis and further topology. The lecture slides are backed up by full notes, a strong team of tutors who will handle all the queries sympathetically and also by a number of online interactive session.


Course Instructor

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Prof. Anant R Shastri

Prof. Anant R Shastri is a retired Emeritus Fellow of Department of Mathematics I.I. T. Bombay. After serving in School of Mathematics T.I.F.R. for 16 years I joined I.I.T. Bombay as a full professor in 1988. Apart from several research papers,I have published three books. Since 2004, I have constantly involved in the activities of ATM schools, The chief activity of these schools is to impart advanced training in Mathematics to Ph. D. students in various universities and research institutions in the country. These activities were initially funded by NBHM and currently adapted by National Centre for Mathematics, I.I.T. Bombay. Over the years, I have taught t roughly the contents of the proposed course more than 20 times to M.Sc/ BTech / MTech and Ph. D. students.CDEEP has recorded my course on Complex Analysis MA205 for B. Tech students. I have offered a course in Algebraic Topology in two parts on NPTEL portal. I strongly believe that especially in these troubled times NPTEL mode of Knowledge-dissemination is the best
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 Course Duration : Jan-Apr 2022
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 Enrollment : 14-Nov-2021 to 31-Jan-2022
 Exam registration : 13-Dec-2021 to 18-Mar-2022
 Exam Date : 24-Apr-2022

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Total Enrollment: 953

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