10-327

DBN: Classes: 2010-11: 10-327/Navigation Additions to the MAT 327 web site no longer count towards good deed points # Week of... Notes and Links 1 Sep 13 About This Class, Monday - Continuity and open sets, Thursday - topologies, continuity, bases. 2 Sep 20 Monday - More on bases, Thursdsay - Products, Subspaces, Closed sets, HW1, HW1 Solutions 3 Sep 27 Monday - the Cantor set, closures, Thursday, Class Photo, HW2, HW2 Solutions 4 Oct 4 Monday - the axiom of choice and infinite product spaces, Thursday - the box and the product topologies, metric spaces, HW3, HW3 Solutions 5 Oct 11 Monday is Thanksgiving. Thursday - metric spaces, sequencial closures, various products. Final exam's date announced on Friday. 6 Oct 18 Monday - connectedness in ${\mathbb {R} }$, HW4, HW4 Solutions, Thursday - connectedness, path-connectedness and products 7 Oct 25 Monday - Compactness of $[0,1]$, Term Test on Thursday, TT Solutions 8 Nov 1 Monday - compact is closed and bounded, maximal values, HW5, HW5 Solutions, Wednesday was the last date to drop this course, Thursday - compactness of products and in metric spaces, the FIP 9 Nov 8 Monday-Tuesday is Fall Break, Thursday - Tychonoff and a taste of Stone-Cech, HW6, HW6 Solutions 10 Nov 15 Monday - generalized limits, Thursday - Normal spaces and Urysohn's lemma, HW7, HW7 Solutions 11 Nov 22 Monday - $T_{3.5}$ and $I^{A}$, Thursday - Tietze's theorem 12 Nov 29 Monday - compactness in metric spaces, HW8, HW8 Solutions, Thursday - completeness and compactness 13 Dec 6 Monday - Baire spaces and no-where differentiable functions, Wednesday - Hilbert's 13th problem; also see December 2010 Schedule R Dec 13 See December 2010 Schedule F Dec 20 Final exam, Monday December 20, 2PM-5PM, at BR200 Register of Good Deeds Add your name / see who's in! See Hilbert's 13th

Introduction to Topology

Department of Mathematics, University of Toronto, Fall 2010

Agenda: Understand "continuity" in the most abstract, learn about "the fundamental groups" and maybe touch "surfaces".

Instructor: Dror Bar-Natan, drorbn@math.toronto.edu (Wiki before Email!), Bahen 6178, 416-946-5438. Office hours: by appointment.

Classes: Mondays 2-3 and Thursdays 2-4 in Sydney Smith 1070.

Teaching Assistant: David Reiss, david.reiss@utoronto.ca, SS 622.

Text

James Munkres' Topology (see Errata). The topology texts by Dugundji and Massey are also recommended, and many other texts are also available. (A useful principle to know is that many math texts are available online. Web search for (name of text + name of author + pdf or djvu).

Further Resources

• Undergraduate Information at the UofT Math Department
• Undergraduate Course Descriptions.
• My 10-327 notebook.
• My 2005-06 Math 1300/427 web site.
• My 2004-05 Math 1300/427 web site.

A note from the TA

Hello all. Just a couple points of possible interest for your problem sets. First, they do not need to be extremely detailed or lengthy, however please make sure that you do mention that an argument comes from a theorem or lemma (unless it is very obvious). You can be very concise as long as you reference your arguments like this. A good length you should aim for is 4 pages hand written. It is also a very good exercise to look over a question you have written out and ask yourself what the main arguments you used were. How can I summarize this argument?

I noticed many students have confused the topology with the basis. The basis generates the topology. For example, not all sets in the product topology of XxY are of the form UxV where U is open in X and V is open in Y. (Consider (0,1)x(0,1) union (2,3)x(2,3) <--- open since it is the union of open sets, yet it cannot be expressed as UxV. Draw a picture if this is unclear).

Cheers