Cosider a set of a closed segments on a real line, each two of them have an intersection. Is it true that there exists a point, which is contained in all of that sets?
My suggestions: 1) First of all, we can build a construction, based on a principe of nested segments (Cauchy-Cantor). But, the thing is that that we can only cope with it in the case, where we work with a finite number of segments.
How to consider this in a common way?
Thank you in advance.