Английская Википедия:Helly space

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

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]

<math> I^I = \prod_{i \in I} I_i </math>

The space II is exactly the space of functions Шаблон:Nowrap. For each point x in [0,1] we assign the point ƒ(x) in Шаблон:Nowrap[3]

Topology

The Helly space is a subset of II. The space II has its own topology, namely the product topology.[2] The Helly space has a topology; namely the induced topology as a subset of II.[1] It is normal Haudsdorff, compact, separable, and first-countable but not second-countable.

References

Шаблон:Reflist


Gelfand–Shilov space