3. Suppose f: RR is continuous and U CR. Assume R has the usual Euclidean metric....

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3. Suppose f: RR is continuous and U CR. Assume R has the usual Euclidean metric. (a) Define U is "open" in R. (b) Proof or counterexample: If U is open, then f(U) is open. (c) Proof or counterexample: If U is open, then f(U) is open. Recall that f-1(U) := {pe Rf(p) U}. E 3. Suppose f: RR is continuous and U CR. Assume R has the usual Euclidean metric. (a) Define U is "open" in R. (b) Proof or counterexample: If U is open, then f(U) is open. (c) Proof or counterexample: If U is open, then f(U) is open. Recall that f-1(U) := {pe Rf(p) U}. E