(I know I'm posting a lot of questions, but I have an exam on Tuesday...)
Find (and draw) a subspace of R^3 that is homeomorphic to the one-point compactification of X when
X = (0,1) x (0,1) \ [0,1/2] x [0,1/2]
X is homeomorphic to $\displaystyle \mathbb{R}^2$. One-point compactification $\displaystyle \mathbb{R}_\infty^{2}$ of $\displaystyle \mathbb{R}^2$ is homeomorphic to two-dimensional sphere $\displaystyle S^2=\{x = (x_1, x_2, x_3) \in \mathbb{R}^3: ||x||=1\}$.