Swayam - Discontinued (Sep 2024)- Topology
offered by Mumbai University

A++ NAAC accredited
Public/Government University
Estd. 1857

Discontinued (Sep 2024)- 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
Mode of learning	Online
Official Website	Go to Website
Credential	Certificate

Discontinued (Sep 2024)- Topology

Table of contents

Overview
Highlights
Course Details
Curriculum
Faculty
+ 1 more item

Discontinued (Sep 2024)- Topology
at
Mumbai University
Highlights

Earn a certificate from Swayam
Learn from industry experts

Discontinued (Sep 2024)- 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

More about this course

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

Discontinued (Sep 2024)- 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

Discontinued (Sep 2024)- 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