Helly space

In mathematics, and particularly functional analysis, the Helly space, named after Eduard Helly, consists of all monotonically increasing functions , where [0,1] denotes the closed interval given by the set of all x such that In other words, for all we have and also if then

Let the closed interval [0,1] be denoted simply by I. We can form the space II by taking the uncountable Cartesian product of closed intervals: : I^I = \prod_{i \in I} I_i The space II is exactly the space of functions . For each point x in [0,1] we assign the point ƒ(x) in

Helly's space is convex as a subset of \mathbb{R}^{[0,1]}.