I'm trying to construct a functions between 2 subsets of the 2d euclidean plane.
The sets are the Hawaiian earring. ie - the countable union of circles with centres (1/n,0) and radius 1/n,
and the countable union of circles of radius n & centres (n,0).
I can construct one using different n's, but is it possible to construct one using just x & y? eg - perhaps some sort of reciprocal function?
It seems like it should be the case, but I just can't see an equation! :-(
Any help would be greatly appreciated. :-)
Many thanks x