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MATH-510: Topology

A continuous deformation (a type of homeomorphism) of a mug into a doughnut (torus) and back.

This is an introductory course in topology, giving the basics of the theory.

Topological spaces, bases and sub-bases, first and second axiom of countability, separability, continuous functions and homeomorphism, finite product space. Separation axioms $(T_0, T_1, T_2)$. Regular spaces, completely regular spaces, normal spaces, compact spaces, connected spaces.

  1. Sheldon Davis, Topology, McGraw-Hill Science/Engineering/Math, 2004.
  2. Seymour Lipschutz, Schaums Outline of General Topology, McGraw-Hill, 2011.
  3. James Munkres, Topology (2nd Edition), Prentice Hall, 2000.
  4. G.F. Simmons, Introduction to Topology and Modern Analysis, Tata McGraw-Hill, 2004. (link)
  5. Stephen Willard, General Topology, Dover Publications, 2004. (link)
  6. M.A. Armstrong, Basic Topology, Springer, 2010.

Presentations

Introduction to Topology Download Presentation (1.6MB)

Selected questions

Selected questions from chapter 05 of [2], that is, Schaums Outline of General Topology.

Starting from page 73. (total 36 questions)

01, 03, 04, 05, 07, 10, 11, 13, 14, 15, 
17, 18, 19, 20, 23, 24, 26, 27, 28, 29,
30, 31, 32, 34, 36, 37, 41, 44, 46, 61,
63, 68, 75, 78, 85, 86. 


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