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 Zx(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 S1.


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.