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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- November 25th 2011, 05:45 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

- November 25th 2011, 07:57 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?

- November 26th 2011, 08:35 AMwopashuiRe: Prove that D is connected