Math 420 ~ Elementary Point-Set Topology
 midterm results


420 Midterm-1 Solutions (Midterm-1 Results)
420 Midterm-2 Solutions (Midterm-2 Results)
420 Final Solutions

Schedule:                                                               
Mondays   10:40-12:30, M-13
Thursdays  11:40-12:30, M-13

Course Content

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

Syllabus:
Week 1-2-3 Intro, topological spaces, basis, subbasis, subspaces, the order topology, the product topology on XxY
Week 3-4-5 Closed sets, interior, boundary, limit points  continuous functions, homeomorphisms, the product topology
Week 5-6-7 The metric spaces, connectedness, connected components, path connectedness, path components
Week 7-8-9 Compactness, sequential compactness, compactness in metric spaces
Week 9 -10-11  Separation axioms: Hausdorff , regular, normal spaces
Week 11-12-13 Urysohn`s Lemma, Tietsze Extension Theorem
Week 13-14 Quotient topology and manifolds (if the time permits)

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 and Grading:
There will be two Midterm Exams (%30 each) and a Final Exam (%40), (also additional %5 from attendance)

Midterm 1:  November 12, 2015 (at 17:40) Room: M-13
                    Topics included: Everything upto ''Continuous Functions''  
 
Midterm 2:  December 11, 2015 (at 17:40) Room: M-13
                    Topics included: Everything upto ''what we saw in class on Dec 3 (Thursday)''
 
Final Exam:  January 15, 2016 (at 09:30) Room: M-102, M-103
                    Topics included: Everything done during the semester


Suggested Exercises:
(Problem numbers are with respect to the second edition of Munkres' book: 2000 Edition !!!)
 P=Problem
(set1) Section 13: P4 (a),(c), P7, P8 (solutions)
(set2) Section 16: P3, P4, P6, P8, P9, P10 (solutions)
 (set3) Section 17: P4, P12, P13, P16, P18, P20 (solutions)
(set4) Section 18: P5, P11, P12,  Section 19: P6, P7 (solutions)
(set5) Section 20: P1 (a), P2, Section 21: P3 (a), P10, Section 23: P4, P6 (solutions)
(set6) Section 24: P1, P2, P3, P9 (solutions)

Notes:
1) More problem sets will appeare as we go.
2) Solutions will be posted (here) one week prior to each coming exam.