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## Homework Statement

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...

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