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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

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Credential

Certificate

Topology
 at 
Mumbai University 
Highlights

  • Earn a certificate from Swayam
  • Learn from industry experts
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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

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

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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

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Topology
 at 
Mumbai University 
Admission Process

    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 

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    Topology
     at 
    Mumbai University 
    Contact Information

    Address

    Fort Campus: Mahatma Gandhi Road
    Kalina Campus: Vidya Nagari, Kalina, Santacruz East

    Mumbai ( Maharashtra)

    Phone
    02226543000

    (For general query)

    0222708700

    (For admission query)

    Go to College Website ->