An introduction to Point-Set-Topology Part-I
Learn topological aspects of metric spaces and important theorems with An introduction to Point-Set-Topology Part-I certification course.
Online
12 Weeks
Free Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study, Virtual Classroom | Video and Text Based |
Course Overview
An introduction to Point-Set-Topology Part-I certification by IIT Bombay via Swayam explores the definition of metric spaces and topological spaces. This is a 12-week online course that deals with topological aspects of metric spaces. An introduction to Point-Set-Topology Part-I certification course will expose students to three crucial theorems on complete metric spaces while providing them with the structure of completion of metric spaces. Through An introduction to Point-Set-Topology Part-I online course, students will get familiar with topological spaces, building new topologies from the old, Bases and subbases, I and II countability, connected and path connectedness, separability, and others.
An introduction to Point-Set-Topology Part-I certification syllabus discusses the meaningful study of analysis and further topology. In the end, the course gives outstanding results such as Urysohn’s lemma and Titze’s extension theorem and some applications. An introduction to Point-Set-Topology Part-I classes are backed up by a strong team of tutors solving all the queries. The classes also include several online interactive sessions.
The Highlights
- Offered by IIT Bombay
- 12 weeks online course
- 3 credit points
- In-person examination
- Certificate of completion
Programme Offerings
- Online interactive sessions
- E-notes
- Expert Tutors
- Offline exams at designated exam centres
- Certification.
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIT Bombay |
Candidates are not required to pay An introduction to Point-Set-Topology Part-I certification fee as this online course is free to enroll in. However, they will have to pay an examination fee of Rs 1,000 to appear in the exam to earn a certificate.
An introduction to Point-Set-Topology Part-I Fee Structure :
Description | Amount in INR |
Exam Fee | Rs. 1000 |
Course Fee | Nil |
Eligibility Criteria
Academic Qualification
- To be eligible for An introduction to Point-Set-Topology Part-I certification by IIT Bombay via Swayam, candidates must have passed 10+2 and have one or two courses in Real Analysis.
- Candidates from various disciplines with modern mathematics such as B.Sc., B. Tech., M. Sc., M. Tech. and PhD, will find this course more beneficial.
Certification Qualifying Details
- Upon completion of An introduction to Point-Set-Topology Part-I online course, students will be provided with an e-certificate, which has the name, photograph and the final exam score with the logos of NPTEL and IIT Bombay.
What you will learn
Pursuing An introduction to Point-Set-Topology Part-I training course will define students about metric spaces and topological spaces. Upon completion, students will:
- Learn topological aspects of metric spaces.
- Learn to create new topologies from the old.
- Get familiar with bases and subbases, separability, connected and path connectedness, I and II countability, Compactness, Lindeloffness, and separation axioms.
- Understand Urysohn’s lemma and Titze’s extension theorem and some applications.
Who it is for
An introduction to Point-Set-Topology Part-I training program is designed for anyone who has completed 12th standard or studied modern mathematics in B.Sc., B. Tech., M. Sc., M. Tech. and Ph.D. Individuals who wish to become engineers in this field will benefit from this course.
Admission Details
Admission to An introduction to Point-Set-Topology Part-I online course from IIT Bombay via Swayam involves the following steps:
Step 1: Candidates’ Registration
Step 2: Online Application Form
Step 3: Admission
Application Details
Applicants may check the below-given instructions to enrol in An introduction to Point-Set-Topology Part-I certification course:
- Visit the official website - https://onlinecourses.nptel.ac.in/noc25_ma10/preview
- Create an account or sign in via Google, Facebook or Microsoft account to register themselves
- Fill up the application by entering the required details
- Submit the form
The Syllabus
Chapter I - Introduction
- Introduction,
- Normed linear spaces (NLS),
- Metric Spaces,
- ε -? Definition of continuity,
- Examples of continuous functions,
- Topological Spaces.
Chapter I - Introduction
- Examples,
- Functions,
- Topology of the n-dim.
- Euclidean space,
- Equivalences of metric spaces,
- Equivalences continued.
Chapter I - Introduction
- Counterexamples,
- Definitions and examples,
- Closed sets,
- Interiors and boundaries,
- Interiors and derived sets.
Chapter I - Introduction
- More examples,
- Metric Trinity,
- Baire’s Category Theorem,
- An Application in Analysis,
- Completion of Metric space.
Chapter II - Creating New Spaces
- Bases and subbases,
- Subbases,
- Box Topology,
- Subspaces,
- Union of spaces.
Chapter II - Creating New Spaces
- Extending neighborhoods,
- Quotient Spaces,
- Product of spaces,
- Study of Products - continued,
- Induced and co-induced topologies.
Chapter III- Smallness Properties of Topological Spaces
- Path Connectivity,
- Connectivity,
- Connected components,
- Connectedness-continued,
- Local Connectivitym,
- More Examples.
Chapter III- Smallness Properties of Topological Spaces
- Compactness and Lindelöfness,
- Compact Metric Spaces,
- Compactness-continued,
- Countability and Separability,
- Types of Topological Properties.
Chapter III- Smallness Properties of Topological Spaces
- Productive Properties,
- Productive Properties-continued,
- Tychonoff Theorem,
- Proof Alexander’s Subbase Theorem.
Chapter IV - Largeness properties
- Fréchet Spaces,
- Hausdorff spaces,
- Examples and Applications,
- Examples and Applications - continued.
Chapter IV - Largeness properties
- Regularity and Normality,
- Characterization of Normality,
- Tietze’s Characterization of Normal Spaces,
- The productiveness of Separation Axioms,
- The Hierarchy.
Chapter V - Topological groups and Topological Vector Spaces
- Topological Groups,
- Topological Groups-continued,
- Topological Groups-continued,
- Topological Vector Spaces,
- Topological Vector Spaces-continued,
- Topological Vector Spaces-continued.
Evaluation process
There is an optional examination for An introduction to Point-Set-Topology Part-I online course through which students can earn the certificate. The exam will be held in person at the designated exam centers. To pass the exam and earn a certificate, students are required to secure at least 10 out of 25% in the best eight assignments out of the total 12 assignments given in the course. Conversely, they have to score a minimum of 30% out of 75% in the proctored certification exam conducted for 100 marks. So, a student must score>= 40/100 to earn the certificate.
Instructors
IIT Bombay Frequently Asked Questions (FAQ's)
Prof. Anant R Shastri, a retired Emeritus Fellow of the Department of Mathematics, IIT Bombay, will be the course instructor.
The duration of An introduction to Point-Set-Topology Part-I certification course is 12 weeks.
Anyone who has passed class 12th can enroll in An introduction to Point-Set-Topology Part-I online course.
The admission process for this online course includes candidates’ registration, filling up the online application form and admission confirmation.
An introduction to Point-Set-Topology Part-I classes are conducted through online interactive sessions by a strong team of tutors.