Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20090311 22:25:17
Prove fixed pointThis 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 Heine–Borel 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 (20090326 15:56:17) #2 20090312 01:40:17
Re: Prove fixed point
Last edited by mathsyperson (20090312 03:24:31) Why did the vector cross the road? It wanted to be normal. #3 20090312 03:14:21
Re: Prove fixed pointApart from the fact that you had amd the wrong way round, you are correct. #4 20090312 03:23:24
Re: Prove fixed pointAh, so I have. Fixed now, thanks. Why did the vector cross the road? It wanted to be normal. 