Let , and let f: D-->R be continuous. Prove that D is connected if { }, the graph of f, is a connected subset of

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- Nov 25th 2011, 06:45 PMwopashuiProve that D is connected
Let , and let f: D-->R be continuous. Prove that D is connected if { }, the graph of f, is a connected subset of

- Nov 25th 2011, 08:57 PMDrexel28Re: Prove that D is connected
This is an if and only if. Let denote the graph, note then that where is the canonical projection onto the first coordinate--why does this tell us 's connected. Conversely, if is connected then where --why is continuous and why does this tell us that is connected?

- Nov 26th 2011, 09:35 AMwopashuiRe: Prove that D is connected