Topology Lectures and Recitations

Fall 2009, Boris Tsirelson

14/12/09 Update:
- Added summaries from 03/12/09 to 10/12/09
- Fixed some errors in several files
- Uploaded summaries in PDF format
24/12/09 Update:
- Added summary page for the midterm exam
25/12/09 Update:
- Uploaded my solution for the exam
31/12/09 Update:
- Added summaries from 23/12/09 to 31/12/09
28/01/10 Update:
- Added summaries from 06/01/10 to 21/01/10
09/02/10 Update:
- Added missing summaries from 16-17/12/09
- Uploaded my solution for the sample exam
15/02/10 Update:
- Added summary page for the final exam
16/02/10 Update:
- Added my solution for the final exam

Please mail me at yoavsha1@post.tau.ac.il if you found any errors, or have any suggestions.
Summary for the midterm exam: doc pdf
Summary for the final exam: pdf
My solution for the 25/12/09 midterm exam: pdf
My solution for the sample exam: pdf
My solution for the final exam: pdf
Note: some of the questions aren't answered in full, but the general idea is given.
If there are any mistakes, please notify me. Thanks.

Lectures:

21/10/09 doc pdf - Introduction, definition of Topological Space, Open Set, Closed Set, Comparison of Topologies
22/10/09 doc pdf - Base of a Topology
28/10/09 doc pdf - Metric Space, Metrizable Space, Subspace Topology
29/10/09 doc pdf - Interior, Exterior, Boundary, Dense Set, Nowhere Dense Set, Limit Point, Isolared Point,
04/11/09 doc pdf - Continuous Map, Homeomorphism
05/11/09 doc pdf - Homeomorphism continued
11/11/09 doc pdf - Connected Space/Set/Component
12/11/09 doc pdf - Path-connected Space/Set/Component
18/11/09 doc pdf - Separation Axioms, Urysohn's Lemma
19/11/09 doc pdf - Urysohn's Lemma continued, Tietze's Extension Theorem
25/11/09 doc pdf - Countability Axioms, Lindelof's Lemma
26/11/09 doc pdf - Urysohn's Metrization Theorem, Compact Set/Space
02/12/09 doc pdf - Compact Set/Space continued, Local Compactness
03/12/09 doc pdf - Compactness continued, Product Space
09/12/09 doc pdf - Product Space continued, Quotient Space
10/12/09 doc pdf - Quotient Space continued
16/12/09 doc pdf - Homotopy, Fundumental Group, Retraction
17/12/09 doc pdf - Fundumental Group continued
23/12/09 doc pdf - Fundamental group continued
24/12/09 doc pdf - Covering space
30/12/09 doc pdf - Covering space continued, Path lifting
31/12/09 doc pdf - Path lifting continued
06/01/09 doc pdf - Path lifting continued, Induced Homomorphism, Conclusions
07/01/09 Hairy Ball Theorem. Missing, for now.
13/01/09 doc pdf - Jordan Theorem
14/01/09 doc pdf - Jordan Theorem continuted
20/01/09 doc pdf - Jordan Theorem continuted, Lesbegue Dimension
21/01/09 Dimensions continued, Missing.

Recitations:

21/10/09 doc pdf - Basic definitions
28/10/09 doc pdf - Metric Space
04/11/09 doc pdf - Interior, Exterior, Boundary, Dense Set, Nowhere Dense Set, Limit Point, Isolared Point,
11/11/09 doc pdf - Continuous Map, Homeomorphism
18/11/09 doc pdf - Connectedness
25/11/09 doc pdf - Separation Axioms, Urysohn's Lemma, Tietze's Extension Theorem
02/12/09 doc pdf - Countability Axioms, Compactness
09/12/09 doc pdf - Compactness, Product Space, Quotient Space
16/12/09 doc pdf - Quotient Space
23/12/09 doc pdf - Quotient Space, Homotopy, Retraction
30/12/09 doc pdf - Fundamental Group, Retraction and Deformation
06/01/09 doc pdf - Covering Space, Path Lifting
13/01/09 doc pdf - Covering Space, Induced Homeomorphism
20/01/09 doc pdf - Geometric Topology