Reference no: EM13296618

1. Prove that, in a topological space X, if U is open and C is closed, then U - C is open and C - U is closed.

2. Which sets are closed sets in the finite complement topology on a topological space X?

3. Let X be a topological space.

(a) Prove that Φ and X are closed sets.

(b) Prove that the intersection of any collection of closed sets in X is a closed set.

(c) Prove that the union of finitely many closed sets in X is a closed set.

4. Show that R in the lower limit topology is Hausdorff.

5. Show that R in the finite complement topology is not Hausdorff.

6. Which sets are closed sets in the particular point topology PPX _p on a set X?