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Helly space : ウィキペディア英語版
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 ''II'' by taking the uncountable Cartesian product of closed intervals:
: I^I = \prod_ I_i
The space ''II'' is exactly the space of functions . For each point ''x'' in () we assign the point ƒ(''x'') in
== Topology ==

The Helly space is a subset of ''II''. The space ''II'' has its own topology, namely the product topology.〔 The Helly space has a topology; namely the induced topology as a subset of ''II''.〔

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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