© | Dror Bar-Natan: Classes: 2004-05: Math 1300Y - Topology: | (9) |
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Assigned Tuesday September 28; due Thursday October 14, 3PM, in class

this document in PDF: HW.pdf

**Required email. ** The class photo will be on
the class' web site in a day or two and you are all required to find
it, find yourself in the photo, and send me an email message (either
using the feedback form on the class' web site or using my regular
email address) with the following information:

- Where are you in the picture? (Say something like ``back row 3rd from the left'', and to be sure, add something descriptive like ``I'm the one with the knotted hair and the Möbius band tattoo on my forehead''.)
- Your name.
- Your email address.
- Your telephone number (optional).
- Which of the last four pieces of information do you allow me to put on the web? If you don't write anything about this, I'll assume that your location in the photo, your name and your email address are public but that your phone number is to be kept confidential.

Your email is due earlier than the rest of this assignment, on Monday October 4 at 4PM. If you aren't in the picture at all, find me before Monday and I'll take a (small) picture of you on the spot and edit it into the main picture.

**Required reading. ** Read, reread and rereread
your notes to this point, and make sure that you really,
really really, really really really understand everything in them. Do the
same every week! Also, read all of Munkres chapter 2.

**Solve the following problems. ** (But submit
only the underlined ones). In Munkres' book (Topology, 2nd edition),
problems 4, __8__ on pages 83-84, problems __4__, 8 on
page 92, problems 6, 7, __13__ on page 101, problems 9, 11, 12,
__13__ on page 112, problems __6__, 7 on page 118 and
problems __3__, 8 on pages 126-128. Also solve (but don't
submit) the following

**Problem. ** Let be the ``Cantor set'', the
closure of the set of real numbers in whose expansion to base 3
doesn't contain the digit (e.g.,
is
in, but
is out). Prove that (taken with
the topology induced from
) is homeomorphic to
(taken with the product topology).

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Dror Bar-Natan 2004-09-27