Let $S^1_{1/n}$ be circles with radius $1/n$ and origin $(1/n,0)$ in the plane. I want to show that the space $X = \cup_{n=1}^\infty S^1_{1/n} \subseteq R^2$, is not a CW complex. I know that one way of proving this is that by showing the $X$ is not a weak topology. I want to know if there is ano...