Banach fixed-point theorem states that:
If $(X,d)$ - complete metric space and $f:X\to X$ is contraction mapping. Then exists unique point $x_0$ such that $f(x_0)=x_0.$
And I have the following question:
Is there incomplete metric space in which every contraction mapping has fixed point?
Can anyone give link to proof of this problem please?
I thought on this problem some hours but I haven't any ideas. I guess that it's really hard problem.