1) Let S and T be subsets of R. Find a counter example for each of the following.

a) If P is the set of all isolated points of S, then P is a closed set

b) If S is closed, then cl (int S) = S

c) if S is open, then int (cl S) = S

d) bd (cl S) = bd S

e) bd (bd S) = bd S

f) bd (S U T) = (bd S) U (bd T)

g) bd ( S-intersect-T) = (bd S)-intersect-( bd T)

2) Prove:

a) S is closed iff S = cl S

b) cl S = S U bd S