1) Determine if the following subsets are open in R 2 (with usual metric), closed in R 2 , or neither.

(a) {(x, y) : |x| + |y| < 1}.

(b) {(x, y) : 0 x e y}.

(c) {(x, y) : 0 y < ex}.

2)Let X = {x R : x 0 or x 1}. Let E = {x X : x 1}. Show that E is an open subset of X.

3) In R, let E = {1, 1 2 , 1 3 , 1 4 , . . .}. Find E and E.

4) Give an example of an infinite union of closed sets that is not closed.