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This is an adaptation of a problem I came across on another forum. The problem was originally stated more generally as follows: if
is a compact subset of with the usual topology and is continuous with , then has a fixed point. Unfortunately this is not quite true: needs to be connected as well as compact. Since, by the HeineBorel theorem, any compact and connected subset of is a closed and bounded interval, I have chosen the interval for convenience.Note also a slight difference in this problem from the originally stated one. In the original problem, the domain of
is a subset of the range of . In my adaptation of the problem, the reverse is the case.Last edited by JaneFairfax (2009-03-25 16:56:17)
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Last edited by mathsyperson (2009-03-11 04:24:31)
Why did the vector cross the road?
It wanted to be normal.
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Ah, so I have. Fixed now, thanks.
I wrote g(x) differently to how I meant it, which is what caused those intervals to be the wrong way round.
Why did the vector cross the road?
It wanted to be normal.
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