Hi. Can anybody help me with this problems:

1. Prove that S^1 \ N is homeomorphic with R. S^1 = {(x,y)|x^2 + y^2=1}, N=(0,1) (S^1\N is circular without one point, (0,1))

2. If set A is countable subset of R^2 (of plane), prove that R^2 \ A is path connected.