Two topological spaces are homeomorphic if there is a bijective continuous map between them that the inverse of this map is continuous too. I think the spaces $[0,1)\times [0,1)$ and $(0,1)\times (0,1)$(as subsets of $\mathbb{R}^2$) are not homeomorphic. But how we can prove that.
The properties of compactness or connectivity cannot help me.
Best Answer
Hint: If you remove $(0,0)$ from the first space, it is still simply connected