Hello!

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