# Odds and ends

The space **R**\**Z** is homeomorphic to a sisjoint union of
infinitely many copies of the interval (0,1). Equivalently, it is
homeomorphic to **Z**x(0,1), and thus homotopy equivalent to
**Z**.

Here is a picture of the effect of the map
e(t) = exp(2p it). On the
left, we see it as a map from **C** to **C**\{0}; on the
right, we see it as a map from **R** to S^{1}.

Here is a curve moving in the complement of a trefoil knot:

Here are the simplices of dimension 0, 1, 2 and 3. You can rotate
them with your mouse.