- 6

- 0

**1. a) Show that (f^-1 S)compliment = f^-1(S compliment) for any set S of reals.**

Then use part a) to show The function f is continuous iff f^-1(S) is closed for every closed set S.

Then use part a) to show The function f is continuous iff f^-1(S) is closed for every closed set S.

**2. inverse image = f^-1(S) = {x: f(x) [tex]\in[/tex] S}**

f is continous iff for every open set U [tex]\in[/tex] the reals, f^-1(U) is open.

f is continous iff for every open set U [tex]\in[/tex] the reals, f^-1(U) is open.