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

106/26Introduction1.1, 1.3, 1.9, 2.2, 2.4, 2.5
206/29§1 to §6Basic set theory: finite and infinite sets3.3, 3.9, 3.11, 4.1, 4.2, 4.9, 4.11
06/30 (x)§1 to §6Basic set theory: countable sets5.4, 6.5, 6.7
07/01No class PC away
07/03No classCollege Holiday
Homework #1, due Tuesday 07/07.
307/06Examples of metric spaces
07/07 (x)Metric spaces and continuous mapsHomework #2, due Monday 07/13 and solution.
07/08§12, §13Topological spaces: topologies and bases
07/10§13Topological spaces: bases13.1, 13.3, 13.4, 13.5, 13.6, 13.8
407/13§14The order topology
07/14 (x)§15The product topology on X × Y16.2, 16.3, 16.6, 16.9
07/15§16The subspace topologyHomework #3, due Monday 07/20 and solution.
07/17§17Closed sets
507/20§17Closure, accumulation points17.3, 17.5, 17.6, 17.7, 17.8
07/21 (x)§17Hausdorff and T1 spaces17.12, 17.14, 17.15, 17.16
07/22Midterm 1 (solution)
07/24Guest lectureThe problem with Topology, by James Binkoski (after T. Maudlin) Homework #4, due Wednesday 07/29 and solution.
607/27§18Continuous maps18.2, 18.3, 18.5, 18.8
07/28 (x)§18Continuous mapsGuest lecture by D. Freund
07/29Not in textHomeomorphisms and the category Top An introduction to categories can be found in course notes by P. Schapira.
07/31§19Products of topological spaces19.1, 19.2, 19.3, 19.4, 19.7, 19.8, 19.10
Homework #5, due Friday 08/07 and solution.
708/03§20The metric topology20.1, 20.3, 20.4, 20.5, 20.6
08/04 (x)§20The metric topology21.3, 21.6, 21.7, 21.8
08/05§21Sequences in metric spaces - Functors Homework #6, due Monday 08/10 and solution.
08/07§23Connected spacesGuest lecture by D. Freund
808/10§24, §25Path connectedness, connected components23.4, 23.5, 23.7, 24.1, 24.2, 24.3
08/11 (x)§26Compact spaces
08/12Midterm 2: in-class (solution), take-home (solution)
08/14§26Compact spaces26.1, 26.2, 26.3, 26.5, 26.7, 26.8
908/17§27Compact subspaces of the real line
08/18 (x)§28Limit point and sequential compactness28.2, 28.6, 28.7
08/19§29Local compactnessHomework #7, due Tuesday 08/25 and solution.
08/21§31 - §34Separation properties and metrizability
1008/24Not in textTopological properties of matrix groups
08/25 (x)No class
08/26Not in textTopological properties of matrix groups
08/29Final examination and solution.