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In mathematics, and particularly functional analysis, the Helly space, named after Eduard Helly, consists of all monotonically increasing functions ƒ : → , where denotes the closed interval given by the set of all x such that 0 ≤ x ≤ 1. In other words, for all 0 ≤ x ≤ 1 we have 0 ≤ ƒ ≤ 1 and also if x ≤ y then ƒ ≤ ƒ.
Let the closed interval be denoted simply by I. We can form the space I by taking the uncountable Cartesian product of closed intervals:
The space I is exactly the space of functions ƒ : →. For each point x in we assign the point ƒ in Ix =.
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