Explain what it means for a topological space to be connected.

Are the following subspaces of the unit square $[0,1] \times[0,1]$ connected? Justify your answers.

(a) $\{(x, y): x \neq 0, y \neq 0$, and $x / y \in \mathbb{Q}\}$.

(b) $\{(x, y):(x=0)$ or $(x \neq 0$ and $y \in \mathbb{Q})\}$.