Hi.....

Let f:A------ R

is a continuous function and A is a connected set

prove that:

{ (x,f(x)):x in A}

is a connected set

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- August 12th 2008, 10:11 PMkarimathconnected set
Hi.....

Let f:A------ R

is a continuous function and A is a connected set

prove that:

{ (x,f(x)):x in A}

is a connected set - August 12th 2008, 10:55 PMparticlejohn
You want to prove that is connected. Consider a continuous surjective map . Let be a separation of into 2 disjoint nonempty sets open in . Then and are disjoint sets whose union is . They are open and form a separation of . Contradiction.

- August 13th 2008, 02:12 AMkarimath
Thank you Particlejohn,

but I want to prove that :

is a connected set in - August 13th 2008, 07:51 AMOpalg
- August 13th 2008, 11:23 AMkarimath
(Clapping) Thank you very much ,Opalg