Let X be a set and t & T be two topologies on X. Prove that if (X,t) is Hausdorff and (X, T) is Compact with t a subset of T, then t=T. (i.e., T is a subset of t).
The Attempt at a Solution
potentially useful theorem: (X,t) Hausdorff and X compact implies that each subset F is compact iff it is closed.
I don't really know which direction to go from here...