Consider ℝ2 with the Euclidean topology and consider ℚ2 ⊂ ℝ2 with the subspace topology. Which of the following statements are true?
1
ℚ2 is connected.
2
If A is a non-empty connected subset of ℚ2, then A has exactly one element.
3
ℚ2 is Hausdorff.
4
{(x, y) ∈ ℚ2 |x2 + y2 = 1} is compact in the subspace topology.