Math 420 Elementary Point-Set Topology
 
 Schedule:
   Tuesdays   09:40-10:30 M-102
  Thursdays  08:40-10:30 M-102

Course Content

Topological Spaces; basis, subbasis, subspaces. Closed sets, limit points. Hausdorff Spaces. Continuous functions, homeomorphisms. Product topology. Connected spaces, compo-nents, path connectedness, path components. Compactness, sequential compactness, compactness in metric spaces. Definition of regular and normal spaces. Urysohn`s Lemma, Tietsze Extension Theorem.

   Syllabus:
Week 1-2 Topological spaces, closed sets, interior, boundary, limit points, examples..
Week 3-4 Metric spaces, Basis, subbasis, subspaces, continuous functions, homeomorphisms
Week 5-6 Product topology, connectedness, connected components, path connectedness, path components
Week 7-8 Compactness, sequential compactness, compactness in metric spaces
Week 9 -10  Separation axioms: Hausdorff , regular, normal spaces
Week 11-12 Urysohn`s Lemma, Tietsze Extension Theorem
Week 13-14 Quotient topology and manifolds 


Course Objective

To introduce and illustrate the main ideas of point-set topology (construction of spaces, connectedness, compactness, separation axioms) and to provide a foundation for further study in analysis, geometry and algebraic topology.

Prerequisite Course: Math 251

Textbook: Topology, James R. Munkres (Part I; Chapter 2,3,4 )

Exams: There will be two Midterm Exams and a Final Exam
Midterm 1   November 10, 2014, Monday, at 17:40  
Midterm 2   December 15, 2014, Monday, at 17:40  
Final            January 09,2015, Friday, at 9:30

Suggested Exercises:
Chapter 2, exercises after section 13: 1,2,3,4,5,6,7,8
                exercises after section 16: 1,2,3,4,8
                exercises after section 17: 1,2,3,4,6,7,8,9,11,12,13,14,15,16,19,20
                exercises after section 18: 1,2,3,4,5,6,7,8,10,11,12
                    exercises after section 20: 1,3,9,11
                    exercises after section 21: 1,2,3,5,6,8,10,11,12
Chapter 3,exercises after section 23:  1,2,3,4,5,6,7,9,10,12
               exercises after section 24:  1,2,3
                   exercises after section 25:  4
             exercises after section 26:  1,2,3,4,5,6,7,8,10,11,12
             exercises after section 27:   2,3,5
                  exercises after section 28:   2,3,6,7