Jan 27 Class canceled due to inclement weather. So the first turn-in homework consists only of Part 1 and is still due to the next Tuesday (or whenever the University will re-open…)

I received the following message from the Office of the Provost: “For full semester classes canceled on Thursday January 27, 2011, Tuesday, May 10 will be the scheduled make-up day.”
So the last day of our class is May 10; on that day we meet in the usual place at the usual time.
Please make appropriate changes in your copies of the Syllabus.

Feb 01 Sections 14, 15, 16. Homework: turn-in and 3,4,6,7 on p. 92

Feb 03 Section 17. Homework: turn in and 3, 6-9, 19, 20 on p. 100-102. The next lecture will be mostly not from the book. Here are notes for those who likes to read in advance: CountabilityConditionsAndConvergence

Feb o8 Countability conditions; convergent sequences in topology (see the handout above). Notes for the next lecture (or two): Mappings

Feb 10 Started to discuss mappings; will conclude the next time.

Feb 15 Finished to discuss mappings. Started products. Products

Feb 17 Finished discussing products.

Notes for the next two (or more) lectures: MetricAndMetrizableSpaces

Feb 22 Started to discuss metric (symmetric, etc.) and metrizable (symmetrizable etc.) spaces. Based on notes (see above), and partially on Sections 20, 21, 30 of Munkres’ book.

Feb 24 Concluded the discussion of metric and metrizable spaces.

Notes for the next several lectures:  Compactness

March 01 Discussed Section 1 and Proof 1 from Section 2 in the notes on compactness.

March 03 Discussed Section 2 of the notes on compactness. Also discussed Exam 1.

March 08 Discussed Section 3 and a part of Section 4 of notes on Compactness.

March 10 Exam1. Have a nice Spring Break. If you still wish to work on difficult problems, there is (optional) homework assignment in the Turn-in section.

Notes for the next several lectures:  AxiomsOfSeparation

March 22 Started to discuss axioms of separation. Discussed the first three sections of the notes on this (except several small topics).

March 24 Discussed cardinal numbers.

March 29 Discussed ordinal numbers.

March 31 Continued with Axioms of Separation. Discussed the Tychonoff Embedding Theorem.

April 05. Almost finished with Axioms of Separation. Discussed Urysohn Metrization Theorem, Urysohn Lemma, Tietze Extension Theorem (without detailed proof), C-embedded sets, the Pressing Down Lemma.

Notes for the next lecture: Local compactness

April 07. Discussed local compactness.

April 12. Started to discuss compactifications. Notes on this topic: Compactifications

April 14. Concluded the discussion of compactifications.

April 19. Recitation before Exam 2; started to discuss connectedness. Notes on this topic: Connectedness (extended version Apr 26)

April 21. Exam 2. No new homework.

April 26. Continued the discussion of connectedness.

April 28. Finished the discussion of connectedness.

Notes for the last lectures: Completeness

Hw2Part1 Hw2Part2 Please correct a misprint in your copies of Homework 2 Part 2. Problem 1 Part 3 must be: Int(A intersection B) = Int A intersection Int B. (In the posted file, it is already corrected). Can you give an example showing why the formula with union instead of intersection was wrong? Hw2Solution

Hw3Part1 Hw3Part2 (Only Part 1 is due next Tuesday)  Hw3Part1Solution

Hw4Part1 Hw3Part2Solution Hw4Part1Solution

Hw5 Hw5Solution

Hw6 Hw6Solution

Hw7 Hw7Solution

Hw8 Hw8solution Problem 1 Part 3 must be “…is normal iff X is T_1 and for every…”

Hw9 Hw9solution

Hw10  Hw10Solution

Hw11

Hw12

Exam 2 will be on Thursday, April 21. Exam 2 will be mostly based on the topics we studied after Exam 1 (the last topic: compactifications). The exam will be in the “book closed, notes closed” form and will be similar in format to Exam 1. Please expect questions of three types: (1) give the definition of a concept or formulate a theorem. (2) Prove or disprove a statement. (3) Determine (with proof) whether or not some topological space has some property. Exam2Solution