en>David Eppstein: /* References */ authorlinks

2013-07-18T07:34:15Z

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← Older revision		Revision as of 09:34, 18 July 2013
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	~~Hello!~~ I ~~am Erick~~. I ~~am happy that~~ I ~~could join to~~ the ~~entire world~~. I ~~live~~ in ~~Great Britain~~, in the ~~south region~~. ~~I dream~~ to ~~check out~~ the ~~various nations, to obtain familiarized with fascinating individuals~~.<br><br>~~Stop by my weblog:~~ [~~http:~~//~~seabb~~.sk/~~php/?a%5B%5D~~=~~%3Ca+href%3Dhttp%3A%2F%2Furin79.com%2F%3Fdocument_srl%3D19892672%3Efha+loan+limits+for+arizona%3C%2Fa%3E best recipes best workout apps for iphone~~]		In mathematics, and particularly [[functional analysis]], the '''Helly space''', named after [[Eduard Helly]], consists of all [[monotonically increasing]] [[function (mathematics)\|function]]s {{nowrap\|1=ƒ : [0,1] → [0,1]}}, where [0,1] denotes the [[closed interval]] given by the [[set (mathematics)\|set]] of all ''x'' such that {{nowrap\|1=0 ≤ ''x'' ≤ 1.}}<ref name="CEIT1">{{Citation\|first=L. A.\|last=Steen\|first2=J. A.\|last2=Seebach\|title=[[Counterexamples in Topology]]\|publisher=Dover\|year=1995\|pages=127 − 128\|ISBN=0-486-68735-X}}</ref> In other words, for all {{nowrap\|1=0 ≤ ''x'' ≤ 1}} we have {{nowrap\|1=0 ≤ ƒ(''x'') ≤ 1}} and also if {{nowrap\|1=''x'' ≤ ''y''}} then {{nowrap\|1=ƒ(''x'') ≤ ƒ(''y'').}}

			Let the closed interval [0,1] be denoted simply by ''I''. We can form the space ''I<sup>I</sup>'' by taking the [[uncountable]] [[Cartesian product]] of closed intervals:<ref name="CEIT2">{{Citation\|first=L. A.\|last=Steen\|first2=J. A.\|last2=Seebach\|title=[[Counterexamples in Topology]]\|publisher=Dover\|year=1995\|page=125 − 126\|ISBN=0-486-68735-X}}</ref>
			:<math> I^I = \prod_{i \in I} I_i </math>
			The space ''I<sup>I</sup>'' is exactly the space of functions {{nowrap\|1=ƒ : [0,1] → [0,1]}}. For each point ''x'' in [0,1] we assign the point ƒ(''x'') in {{nowrap\|1=''I<sub>x''</sub> = [0,1].}}<ref>{{Cite book\|first=R\|last=Penrose\|title=The Road to Reality: A Complete guide to the Laws of the Universe\|publisher=Vintage Books\|year=2005\|pages=368 − 369\|isbn=0-09-944068-7}}</ref>

			== Topology ==

			The Helly space is a subset of ''I<sup>I''</sup>. The space ''I<sup>I''</sup> has its own topology, namely the [[product topology]].<ref name="CEIT2"/> The Helly space has a topology; namely the [[induced topology]] as a subset of ''I<sup>I''</sup>.<ref name="CEIT1"/>

			== References ==
			{{reflist}}

			[[Category:Functional analysis]]

155.247.31.240 at 14:12, 23 August 2012

2012-08-23T14:12:55Z

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Hello! I am Erick. I am happy that I could join to the entire world. I live in Great Britain, in the south region. I dream to check out the various nations, to obtain familiarized with fascinating individuals.<br><br>Stop by my weblog: [http://seabb.sk/php/?a%5B%5D=%3Ca+href%3Dhttp%3A%2F%2Furin79.com%2F%3Fdocument_srl%3D19892672%3Efha+loan+limits+for+arizona%3C%2Fa%3E best recipes best workout apps for iphone]

Evenly spaced integer topology - Revision history

en>David Eppstein: /* References */ authorlinks

155.247.31.240 at 14:12, 23 August 2012