Oral test 3 on material up through and including Problem Set 6.
Review definitions, examples, and reasons why statements are true or false
from the recent two problem sets and solutions, the WebCT quiz, 
and class notes.
<p>
This test will be closed to notes and help and comments can only come from
Dr. Sarah.

<p>Review especially the <b>definitions</b> that I listed for
the material from <a href="oraltest.html">Oral test 1</a> 
and <a href="oraltest2.html">Oral test 2</a>
as it is likely that some of these definitions will reappear on this test.
In addition, make sure that you also know
<li>Numerous definitions of continuous
<li>Definition of 1-1
<li>Definition of onto
<li>Definition of homeomorphism
<li>Definition of connected
<li>Definition of a separation
<li>Definition of path connected


<br><br>In addition, be sure to know 
numerous examples for each of the following
(or an explanation of why numerous examples are not 
possible): <br><br>
<li>Two spaces that are subspaces of R and are homeomorphic.
<li>Two spaces that are subspaces of R and are not homeomorphic.
<li>Two spaces that are subspaces of R<sup>2</sup>
 and are homeomorphic.
<li>Two spaces that are subspaces of R<sup>2</sup>  and are not homeomorphic.
<li>A space that is connected but not path connected
<li>A space that is path connected but not connected
<li>A space that is neighter connected nor path connected
<li>A space that is both connected and path connected
<br><br>
For each example, you need to demonstrate why it satisfies the criterion.
<br><br>
In addition, know whether the following are homeomorphic and why or why not.
<br><br>
<li>R with the standard topology and R_cf with the finite complement topology. 
<li>S<sup>1</sup> and [0,1)
<li>The Zariski topology on R<sup>2</sup>
 and the finite complement topology on 
R<sup>2</sup>


<p>
In each case, I will be looking for clarity and depth, and a clear
demonstration that you understand "why".  
Don't be afraid of repetition - when you get up to the board, 
restate your question, explain the relevant background material, answer
your question, and then review what you did and explain again 
how it relates to the original question.  Make some connections,
and relate it to big picture ideas or metaphors too.  I am looking for:


<br>Clarity
<br>Depth
<br>Your demonstration of an understanding of 
relevant definitions and the problem and its correct solution without help from
others
<br>Eye Contact
<br>Included enough repetition
<br>Included connections and big picture ideas or metaphors