Interested in this College?
Get updates on Eligibility, Admission, Placements Fees Structure

Quick Facts

Medium Of Instructions	Mode Of Learning	Mode Of Delivery
English	Self Study	Video and Text Based

Course Overview

Learners pursuing the Topology Certification will encounter crucial ideas like continuity, convergence, compactness, separability, and connectedness that are crucial in numerous applications of mathematics.

Students will learn definitions in Topology Classes and build examples and counterexamples based on definitions. Topology Certification Syllabus includes a variety of definitions, theorems, continuity, convergence, and their justifications. All students get a Topology Certification by University of Mumbai under the Swayam Initiative by the Government of India.

The Highlights

Provided by University of Mumbai
Online course
12 Weeks course
Learn at your own pace
Shareable Certificate
Expert Lectures

Programme Offerings

video lectures
Study Materials

Courses and Certificate Fees

Fees Informations	Certificate Availability	Certificate Providing Authority
INR 1000	yes	Mumbai University

If you want a certificate, you have to register and write the final exam which will be notified well in advance, however it is optional for a fee of Rs 1000.

The Topology Certification Fees is nil. It's open for all interested candidates.

Topology Certification Fees

Description	Amount
Course Fees	Free
Course Fees (with certification)	INR 1000/-

Eligibility Criteria

Certificate Qualifying Details

E-certificates will be issued to all such participants who get 30% weightage internal assessment and 70% weightage main examination.

Work experience

No prior work experience is necessary to register in this certificate programme.

What you will learn

The types and topological properties of these subsets will be covered in the Topology Certification Course along with the question of whether intervals are formed by their union, intersection, or complement. Students will benefit from Topology Training that explains the concepts of a neighbourhood of a point on a line, limit points of a set, and the Bolzano Weierstrass Theorem.

The following learning outcomes are achieved upon successful conclusion of this Topology Certification:

Understand standard concepts of Set theory
Analyse structure of Sets and other abstract algebraic structures
Describe when a set is open and establish the relationship between open and closed sets

Who it is for

If the appropriate students apply for the online course Topology, there will be excellent employment prospects.

Admission Details

Students are urged to enrol in Topology Certification by taking the following measures as soon as the course's admission period opens.

Step 1: Visit the official website

Step 2: Fill up the application form

Step 3: Upload all necessary documents

Step 4: Pay the required fee online (if you need certification)

The Syllabus

Set Theory, Relations and Functions

Metric spaces

Interior/Boundary/limit points, closure

Sequences, Convergence and properties

Completion, Compactness and Connectedness of Metric Spaces.

Compactness & Equivalent Conditions for Compact Metric Spaces

Topological Spaces, Basis, suspaces, product topology

Separation axioms, First and Second Countability, Baire space

Compactness in general topological spaces, Continuity and compactness,Subspace, Lebesgue covering lemma.

Tube lemma and it's application, Metrizable spaces and heriditary properties of topological spaces.

Product of Regular spaces, Connectedness.

Quotient topology, quotient spaces and Tychonoff theorem.

Evaluation process

Yes, there will be assessments and one Final Exam.

Instructors

Mumbai University Frequently Asked Questions (FAQ's)

1: What is topology in mathematics?

Topology, also known as rubber-sheet geometry, is the study of the characteristics of spaces that are invariant under any continuous deformation.

2: How are the classes for Topology Online Course being held?

The classes are administered through pre-recorded videos and lectures.

3: Is topology pure maths?

Pure mathematics subfields of geometry and topology make up a very active area of central significance in the current mathematical landscape.

4: Who is teaching faculty for this course?

The instructor for this course is Mandar Bhanushe - Mathematics Faculty at the Institute of Distance and Open Learning, University of Mumbai.

5: What are the applications of topology?

Riemann surfaces in complex analysis, Differential equations, dynamical systems, and knot theory are a few of the varied applications. It is also employed in string theory, a branch of physics, to explain the universe's space-time organisation.