[Thm]任意两个可数的度量空间, 如果没有孤立点的话, 则一定是同胚的.
定理[Serpinski]. 任意两个可数的度量空间, 如果没有孤立点的话, 则一定是同胚的.
References:
http://math.stackexchange.com/questions/72143/is-there-a-countable-regular-space-with-no-isolated-points-which-is-not-homeomo
Answer