This is the official homepage for MAT327 at the University of Toronto for the summer 2019 term.

All course information other than grades will be posted here and only here.

**6 September** - Made section 19 of the notes available. Sorry about that!

**4 September** - I've just uploaded the 19th section of my lecture notes and Big List, on the subject of compactifications, for any students who may be interested. Note that I'm planning on leaving the Piazza forum active if you still have questions about exercises, though I cannot guarantee fast responses at this time.

**17 August** - As I mentioned in an email announcement last week, I will be holding one more session of office hours, tomorrow (Monday) 1-3pm in the usual place (HU1018). As always, if you need to ask other questions, feel free to use Piazza. I will be checking it periodically today, and often on Tuesday and Wednesday.

**8 August** - Tutorial problems for this week's tutorial. Sorry they're a bit late! 16.1.8, 16.2.8, 16.2.9, 17.1.2, 18.13. Recall that for tomorrow's lecture I'm going to be teaching for about an hour and a half, after which all students will attend one tutorial until 3pm.

**5 August** - Quiz 4 took place in tutorials this past Friday. The quizzes and some sample solutions can be found on the Quizzes tab.

**26 July** - I have just posted all the remaining sections of the lecture notes and Big List. These will take us through the last two weeks of the course. Normally I would space out the posting of these a bit more, but since we're a little bit pressed for time right now, I'm happy to make them all available right now. Feel free to read ahead!

**25 July** - The final exam schedule has now been posted. You can see it here. Our exam is scheduled for Wednesday, 21 August, from 7pm to 10pm, in EX100.

**24 July** - **Remember**: We agreed to move Quiz 4 to next week. This week there is a regular tutorial. Problems to prepare for this week's tutorial: 14.1.15 and 14.2.11.

**20 July** - Section 14 of the lecture notes and Big List are now available.

**17 July** - Section 13 of the lecture notes and Big List are now available.

**17 July** - Tutorial problems for this week's tutorial: 11.1 and 12.10 (particularly the first two parts).

**15 July** - Quiz 3 took place in tutorials this past Friday. The quizzes and some sample solutions can be found on the Quizzes tab.

**11 July** - Section 12 of the lecture notes and Big List are now available.

**9 July** - Section 11 of the lecture notes and Big List are now available.

**3 July** - Tutorial problems for this week's tutorial: 10.7, 10.8, 10.9, 10.15.

**25 June** - The tenth section of the lecture notes and Big List are now available.

**19 June** - I've added a new tab to the web page, on which I will post a short summary of which sections of my notes are covered in each lecture. This was suggested by a student (using the anonymous feedback form!) and I think it's a great idea. I'm also willing to post students' notes from lectures if they're interested. Read what I wrote on that page for more info about this.

**18 June** - The midterm test took place yesterday, Momday 17 June. You can find the test and some sample solutions on the newly-created Midterm tab on this site.

It was clear by the end of the test that I made the test a bit too long. I want to reassure you that I recognise this, and that it was definitely not my intention to make it too long. My apologies if the test was unpleasant experience. My promise from the beginning of the course was to try to make it fair, and by virtue of being too long, this test was not fair. Once it is marked and I have the data to work with, I will think of a way to adjust the grades to compensate for my mistake here.

In the meantime, rest assured that your final mark after adjustment will reflect your abilities as best as I can make it. In particular, please don't make any rash decisions about dropping the course until the marks are in. I hope the two-week break is relaxing for you all.

**16 June** - As mentioned in class last week, I'm going to be holding some bonus office hours tomorrow (Monday) before the midterm. They will be from 1-3pm least, possibly as long as 1-4pm. I won't have a chance to book my usual room (HU1018), so let's say that the office hours will be there unless someone else is using that room, in which case we'll move out to the 10th floor lounge.

**13 June** - The problems for tomorrow's tutorial are: 8.7, 9.1, 9.4, and 9.7. I double-checked them this time!

**12 June** - The midterm's date, time, and location have been finalized. It will take place 6-8p on Monday 17 June, in **BA1180**. If you have any conflicts with this time, please let me know as soon as possible and we will work out some sort of accommodation (most likely an earlier sitting on the same day). Apologies for the delay in finalizing this information.

**10 June** - The time and date of the midterm has been finalized for **6-8pm on Monday, 17 June**. Note that this is different from the original date I had hoped for. I explained in class this past Friday why I was unable to book it for Tuesday the 18th, and we agreed on this alternative time and date. The location is still to be determined, pending room booking. I'll update this page, and send a coursewide announcement, as soon as I have finalized the location. (I'll also update the syllabus to reflect the new date later today.)

**10 June** - Section 9 of the Big List and lecure notes are now available. These will be the last sections posted before the midterm. I've also posted a supplementary note on products of ccc spaces for any students who may be interested. These notes rely on concepts we haven't defined yet, so feel free to research those concepts ahead of time or simply wait until we have covered them.

**7 June** - Quiz 2 took place in tutorials this afternoon. The quizzes and some sample solutions can be found on the Quizzes tab.

This information is contained in the syllabus. It is reproduced here for your convenience.

**Ivan Khatchatourian**is the course coordinator.- ivan [at] math [dot] toronto [dot] edu

Lectures:

**W1-3**and**F12**in**MP137**.- Tutorials:
- TUT0101 -
**F1**in**BA2195** - TUT0201 -
**F2**in**BA2195**

- TUT0101 -
Office hours with Ivan:

**W4 and R1-3**All office hours will take place in

**HU1018**. If you cannot make any of these times, contact me by email and arrange a meeting at a mutually convenient time.

- Lecture notes
- 01: Introduction
- 02: Bases of topologies
- 03: Closed sets and closures
- 04: Countability
- 05: Sequences, weak T-axioms, and first countability
- 06: Continuity and homeomorphisms
- 07: Subspaces
- 08: Finite products
- 09: Stronger separation axioms
- 10: Orders and omega_1
- 11: The Axiom of Choice and Zorn's Lemma
- 12: Metric spaces and metrizability
- 13: Urysohn's Lemma
- 14: Arbitrary products
- 15: The Urysohn Metrization Theorem
- 16: Compactness
- 17: Tychonoff's Theorem, and some properties related to compactness
- 18: Connectedness
- 19: Compactifications

- Supplementary notes
Things You Should Know

This document lists some of the basic concepts with which students entering this course are assumed to be familiar.

**Quiz 1**took place on Friday, 24 May.- Coverage: Up to about half way through section 4 (i.e., up to and including Friday 17 May's lecture).
- Tutorial T0101 wrote this quiz. Here are some sample solutions.
- Tutorial T0201 wrote this quiz. Here are some sample solutions.

**Quiz 2**will take place on Friday, 7 June.- Coverage: Up to the end of section 6.
- Tutorial T0101 wrote this quiz. Here are some sample solutions.
- Tutorial T0201 wrote this quiz. Here are some sample solutions.

**Quiz 3**will take place on Friday, 12 July.- Coverage: Section 10.
- Tutorial T0101 wrote this quiz. Here are some sample solutions.
- Tutorial T0201 wrote this quiz. Here are some sample solutions.

**Quiz 4**will take place on Friday, 2 August.**Note that this quiz was moved one week later**- Coverage: Up to the end of section 14.
- Tutorial T0101 wrote this quiz. Here are some sample solutions.
- Tutorial T0201 wrote this quiz. Here are some sample solutions.

- The midterm test took place on Monday, 17 June, from 6:10-8pm.
- Coverage: Up to the end of section 9, though not including any Big List problems after problem 9.7.
- Here is the test. Here are some sample solutions.

It was suggested that for each lecture I post a short summary of what chapters/sections of my notes are covered in each lecture. This is a great idea, so I'll start doing that here. I'll also be posting any in-class notes from students who wish to make them available for the benefit of other students. I have a tendency to say a lot of things that I don't write on the board in class, so in-class notes may be very valuable.

**DISCLAIMER:** The in-class notes made by students and published here are the work of students. I have not edited them in detail for mathematical accuracy or style.

Any students who are willing to have their notes posted publicly should email them to me as a PDF (one PDF per lecture) and include the date of the lecture. Also mention if you're willing to have your name posted with them (you may post them anonymously). I am willing to post handwritten notes provided they are neat, legible, and scanned/photographed well. In particular, your notes do not have to be typed, but if they are typed it must be with LaTeX and your notation must agree with the notation of my notes (`\mathcal{T}`

for a topology, etc.).

**WEEK 1****Lecture 1**- Wed, 8 May- Introductory remarks
- Coverage: Chapter 1, up to the end of section 3.
- In-class notes by Asad Durrani.

- Lecture 2 - Fri, 10 May
- Coverage: Finished Chapter 1, and about the first four pages of Chapter 2.
- In-class notes by Asad Durrani.

**WEEK 2****Lecture 3**- Wed, 15 May- Coverage: Finished Chapter 2, and all of Chapter 3.
- In-class notes by Asad Durrani.

**Lecture 4**- Fri, 10 May- Coverage: Approximately the first five sections of Chapter 4.
- In-class notes by Asad Durrani.

**WEEK 3****Lecture 5**- Wed, 22 May- Coverage: Finished Chapter 4, and about the first four sections of Chapter 5.
- In-class notes by Asad Durrani.

**Lecture 6**- Fri, 24 May- Coverage: Finished Chapter 5.
- In-class notes by Asad Durrani.

**WEEK 4****Lecture 7**- Wed, 29 May- Coverage: Approximately the first five sections of Chapter 6.
- In-class notes by Asad Durrani.

**Lecture 8**- Fri, 31 May- Coverage: Finished Chapter 6.
- In-class notes by Asad Durrani.

**WEEK 5****Lecture 9**- Wed, 5 June- Coverage: All of Chapter 7.
- In-class notes by Asad Durrani.

**Lecture 10**- Fri, 7 June- Coverage: All of Chapter 8.

- Coverage: All of Chapter 8.

**WEEK 6****Lecture 11**- Wed, 12 June- Coverage: Chapter 9, up the end of section 3.

**Lecture 12**- Fri, 14 June- Coverage: Section 4 of Chapter 9.

**WEEK 7****Lecture 13**- Wed, 3 July- Coverage: Chapter 10, up to the definition of a well-order.

**Lecture 14**- Fri, 5 July- Coverage: Definition of omega_1

- Coverage: Definition of omega_1

**WEEK 8****Lecture 15**- Wed, 10 July- Coverage: Finished Chapter 10, started Chapter 11.

**Lecture 16**- Fri, 12 July- Coverage: Finished Chapter 11.

- Coverage: Finished Chapter 11.

**WEEK 9****Lecture 17**- Wed, 17 July- Coverage: Chapter 12.

**Lecture 18**- Fri, 19 July- Coverage: Chapter 13 (slightly abridged, as I was delayed getting to class)

- Coverage: Chapter 13 (slightly abridged, as I was delayed getting to class)

**WEEK 10****Lecture 19**- Wed, 24 July- Coverage: Chapter 14, roughly to the end of section 4.

**Lecture 20**- Fri, 26 July- Coverage: Chapter 14, up to about half way through section 7.

- Coverage: Chapter 14, up to about half way through section 7.

**WEEK 11****Lecture 21**- Wed, 31 July- Coverage: Finished chapter 14 and 15.

**Lecture 22**- Fri, 2 August- Coverage: Chapter 16, almost to the end of section 3.

- Coverage: Chapter 16, almost to the end of section 3.

**WEEK 12****Lecture 23**- Wed, 7 August- Coverage: (Hopefully) finish chapter 16 and chapter 17.

**Lecture 24**- Fri, 9 August- Coverage: Chapter 18.