- #1
im2fastfouru
- 6
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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.
2. inverse image = f^-1(S) = {x: f(x) [tex]\in[/tex] S}
f is continuous iff for every open set U [tex]\in[/tex] the reals, f^-1(U) is open.
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 continuous iff for every open set U [tex]\in[/tex] the reals, f^-1(U) is open.