# Swayam - Topology offered by Mumbai University

• A++ NAAC accredited
• State University
• Estd. 1857

## Topology at Mumbai University Overview

Equip with solid understanding of fundamental topological principles providing a strong foundation for to approach problems and analysis within mathematics and its applications
 Duration 12 weeks Total fee Free Mode of learning Online Official Website Explore Free Course Credential Certificate

## Topology at Mumbai University Highlights

• Earn a certificate from Swayam
• Learn from industry experts

## Topology at Mumbai University Course details

Who should do this course?
• For individuals who want to enhance their knowledge & skills in the field
What are the course deliverables?
• Understand standard concepts of Set theory
• Analyse structure of Sets and other abstract algebraic structures
• Understand definitions; construct examples and counter examples based on definitions
• Develop intuition regarding proofs, make arguments based on logic
• Review of set theory, relations and functions
• Introduction to topology of metric spaces
• Introduction to topological spaces
• Continuity, convergence
• Subspaces, product spaces, quotient spaces
• Connectedness and Compactness
• In this course aspirants shall come across important notions like continuity, convergence, compactness, separability, connectedness which are important in many applied areas of Mathematics
• We shall do various definitions, theorems and their proofs from topics in Topology

## Topology at Mumbai University Curriculum

WEEK 1 :Set Theory, Relations and Functions

WEEK 2 :Metric spaces

WEEK 3 :Interior/Boundary/limit points, closure

WEEK 4 :Sequences, Convergence and properties

WEEK 5 :Completion, Compactness and Connectedness of Metric Spaces

WEEK 6 :Compactness & Equivalent Conditions for Compact Metric Spaces

WEEK 7 :Topological Spaces, Basis, suspaces, product topology

WEEK 8 :Separation axioms, First and Second Countability, Baire space

WEEK 9 :Compactness in general topological spaces, Continuity and compactness,Subspace, Lebesgue covering lemma

WEEK 10 :Tube lemma and it's application, Metrizable spaces and heriditary properties of topological spaces

WEEK 11 :Product of Regular spaces, Connectedness.WEEK 12 :Quotient topology, quotient spaces and Tychonoff theorem

## Topology at Mumbai University Faculty details

Mandar Bhanushe
Mandar Bhanushe has experience of 15 years teaching both at the undergraduate and postgraduate level He was winner of National level Indian Education Award at the Indian Education Congress in May 2013 for conducting Best Webinar Series in the subject of Mathematics

## Topology at Mumbai University Entry Requirements

Eligibility criteria

## Important Dates

May 24, 2023
Online-Phonetics and Phonology (Part-time) Admission process start date
Aug 6, 2023
Online-Phonetics and Phonology (Part-time) Commencement
Nov 10, 2023
(Life Skills Education in English & Marathi) Last date to apply

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## Topology at Mumbai University Contact Information

Kalina Campus: Vidya Nagari, Kalina, Santacruz East

Mumbai ( Maharashtra)

Phone
02226543000

(For general query)

0222708700