Helly space

In mathematics, and particularly functional analysis, the Helly space, named after Eduard Helly, consists of all monotonically increasing functions, where 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 be denoted simply by I. We can form the space I^I by taking the uncountable Cartesian product of closed intervals:
The space I^I is exactly the space of functions. For each point x in we assign the point ƒ in
Helly's space is convex as a subset of.

Topology

The Helly space is a subset of I^I. The space I^I has its own topology, namely the product topology. The Helly space has a topology; namely the induced topology as a subset of I^I. It is normal Haudsdorff, compact, separable, and first-countable but not second-countable.