In mathematics, and particularly functional analysis, the Helly space, named after Eduard Helly, consists of all monotonically increasing functions ƒ : [0,1] → [0,1], where [0,1] denotes the closed interval given by the set of all x such that 0 ≤ x ≤ 1.
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:[2] The space II is exactly the space of functions ƒ : [0,1] → [0,1].
[3] The Helly space is a subset of II.
[1] It is normal Haudsdorff, compact, separable, and first-countable but not second-countable.