Gave the definitions of continuous function and homeomorphism, and gave some examples.

<br><br>
In Topology two spaces are considered to be "the same" precisely when they are homeomorphic. A property is said to be <I>topological</I> if, whenever some space X possesses the property then so too do all spaces Y that are homeomorphic to X. (So, for instance, the "sum of the interior angles" is not a topological property of a polygon since it is 180 degrees for a triangle, and 360 degrees for a quadrangle, and yet a triangle is homeomorphic to a quadrangle.)

<br><br>
I didn't have time to show the classic example of a  <a href="http://hamilton.nuigalway.ie/teachingWeb/MA342/mug.gif">homeomorphism between a doughnut and a coffee mug</a> so please take a look at it  on-line.