Consider ([0, 1], T1), where T1 is the subspace topology induced by the Euclidean topology on ℝ, and let T2 be any topology on [0, 1]. Consider the following statements:
P : If T1 is a proper subset of T2, then ([0, 1], T2) is not compact.
Q : If T2 is a proper subset of T1, then ([0, 1], T2) is not Hausdorff.
Then
1
P is TRUE and Q is FALSE
2
Both P and Q are TRUE
3
Both P and Q are FALSE
4
P is FALSE and Q is TRUE