Quote:
Originally Posted by R.D. Silverman
Looks good to me.
I don't understand the hint either.
Compact sets have finite covers by open sets

If you don't understand something, then ask for explanation.
Any subset of a topological space has finite cover by open sets ( for example whole space ), not only compact subsets. We all know what you meant and all know that you used irony again writing something different than it should be.
So, 3 worthless sentences in 2 short posts.