## Math 54: Topology

### Summer 2015

General Info
Diary

The homework problems are to be found in the textbook; 'a.b' means 'Problem b in Paragraph a'. It is strongly suggested that you treat all the problems listed here.
Policy: homework should be submitted no later than 5pm on the due date. Let your instructor know in advance if you feel that you need extra time.

 wk date reading topic homework / comments 1 06/26 Introduction 1.1, 1.3, 1.9, 2.2, 2.4, 2.5 2 06/29 §1 to §6 Basic set theory: finite and infinite sets 3.3, 3.9, 3.11, 4.1, 4.2, 4.9, 4.11 06/30 (x) §1 to §6 Basic set theory: countable sets 5.4, 6.5, 6.7 07/01 No class PC away 07/03 No class College Holiday Homework #1, due Tuesday 07/07. 3 07/06 Examples of metric spaces 07/07 (x) Metric spaces and continuous maps Homework #2, due Monday 07/13 and solution. 07/08 §12, §13 Topological spaces: topologies and bases 07/10 §13 Topological spaces: bases 13.1, 13.3, 13.4, 13.5, 13.6, 13.8 4 07/13 §14 The order topology 07/14 (x) §15 The product topology on X × Y 16.2, 16.3, 16.6, 16.9 07/15 §16 The subspace topology Homework #3, due Monday 07/20 and solution. 07/17 §17 Closed sets 5 07/20 §17 Closure, accumulation points 17.3, 17.5, 17.6, 17.7, 17.8 07/21 (x) §17 Hausdorff and T1 spaces 17.12, 17.14, 17.15, 17.16 07/22 Midterm 1 (solution) 07/24 Guest lecture The problem with Topology, by James Binkoski (after T. Maudlin) Homework #4, due Wednesday 07/29 and solution. 6 07/27 §18 Continuous maps 18.2, 18.3, 18.5, 18.8 07/28 (x) §18 Continuous maps Guest lecture by D. Freund 07/29 Not in text Homeomorphisms and the category Top An introduction to categories can be found in course notes by P. Schapira. 07/31 §19 Products of topological spaces 19.1, 19.2, 19.3, 19.4, 19.7, 19.8, 19.10 Homework #5, due Friday 08/07 and solution. 7 08/03 §20 The metric topology 20.1, 20.3, 20.4, 20.5, 20.6 08/04 (x) §20 The metric topology 21.3, 21.6, 21.7, 21.8 08/05 §21 Sequences in metric spaces - Functors Homework #6, due Monday 08/10 and solution. 08/07 §23 Connected spaces Guest lecture by D. Freund 8 08/10 §24, §25 Path connectedness, connected components 23.4, 23.5, 23.7, 24.1, 24.2, 24.3 08/11 (x) §26 Compact spaces 08/12 Midterm 2: in-class (solution), take-home (solution) 08/14 §26 Compact spaces 26.1, 26.2, 26.3, 26.5, 26.7, 26.8 9 08/17 §27 Compact subspaces of the real line 08/18 (x) §28 Limit point and sequential compactness 28.2, 28.6, 28.7 08/19 §29 Local compactness Homework #7, due Tuesday 08/25 and solution. 08/21 §31 - §34 Separation properties and metrizability 10 08/24 Not in text Topological properties of matrix groups 08/25 (x) No class 08/26 Not in text Topological properties of matrix groups 08/29 Final examination and solution.