Question 6:
4 Marks
Let $\epsilon > 0$ and $Q = [(-3, 5) \cup (8, \frac{19}{2})] \cap (2, 9]$. Which of the following sets
$T_j$, ($j = 1, \dots, 4$) are neighborhoods of the given point $a$.
(1) $T_1 = Q$, $a = 7$;
(2) $T_2 = Q$, $a = 3$.
(3) $T_3 = \left(\frac{-2 - 3\epsilon}{3}, \frac{4 + 5\epsilon}{2}\right)$, $a = 2$;
(4) $T_4 = \left(\frac{-3 - 3\epsilon}{2}, \frac{3 + 7\epsilon}{2}\right)$, $a = \epsilon + 2$.
