### Problem Set 3

Munkres
p. 83 # 7

Munkres p. 83 - 84 # 8 (both parts a and b)

Prove that [a,b) with reals a < b is neither open nor closed in the standard
topology on the reals, but that it is both open and closed in the lower limit
topology on the reals.

**Additional grad problem, which is an extra credit problem for
undergrads**:
Munkres p. 83 # 6