Let

$A = \{(x,y) \in \mathbb{R}^2 | (x+1)^2 + y^2 = 1\}$,\\

$B = \{(x,y) \in \mathbb{R}^2 | (x-1)^2 + y^2 = 1\}$, and\\

$C = \{(x,y) \in \mathbb{R}^2 | x^2 + y^2 = 1\}$.\\

Define $N = A \cup B$

and let $N$ and $C$ be given subspaces of ${\mathbb{R}}^2$, where ${\mathbb{R}}^2$ is given the standard topology. Show that $N$ is not homeomorphic to $C$.

PICTURE ATTACHED!