§ Shrinking wedge of circles / Hawaiian earring (TODO)
I've been trying to make peace with the fact that countably infinite wedge of circles
is so different from the hawaiian earring. Here are some thoughts:
- Topology on the hawaiian earring is very different. Eg: small opens around the center of infinitewedge is contractible, while no small open around the origin of the hawaiian earring is contractible.
- We can take infinite products of group elements in the hawaiian earring, since the radii decrease.For example, we can take a loop at each circle of radius by making it traverse the circleof radius in the interval , and stay at at .