Helly space (original) (raw)
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. In other words, for all 0 ≤ x ≤ 1 we have 0 ≤ ƒ(x) ≤ 1 and also if x ≤ y then ƒ(x) ≤ ƒ(y). 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:
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dbo:abstract | 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. In other words, for all 0 ≤ x ≤ 1 we have 0 ≤ ƒ(x) ≤ 1 and also if x ≤ y then ƒ(x) ≤ ƒ(y). 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: The space II is exactly the space of functions ƒ : [0,1] → [0,1]. For each point x in [0,1] we assign the point ƒ(x) in Ix = [0,1]. (en) |
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dbo:wikiPageWikiLink | dbr:Cartesian_product dbr:Product_topology dbr:Compact_space dbr:Normal_space dbr:Separable_space dbr:Second-countable_space dbr:Function_(mathematics) dbr:Functional_analysis dbr:Eduard_Helly dbr:Closed_interval dbc:Functional_analysis dbr:Induced_topology dbr:Set_(mathematics) dbr:First-countable_space dbr:Uncountable dbr:Monotonically_increasing |
dbp:wikiPageUsesTemplate | dbt:Reflist |
dct:subject | dbc:Functional_analysis |
rdfs:comment | 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. In other words, for all 0 ≤ x ≤ 1 we have 0 ≤ ƒ(x) ≤ 1 and also if x ≤ y then ƒ(x) ≤ ƒ(y). 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: (en) |
rdfs:label | Helly space (en) |
owl:sameAs | freebase:Helly space wikidata:Helly space https://global.dbpedia.org/id/4m291 |
prov:wasDerivedFrom | wikipedia-en:Helly_space?oldid=990502147&ns=0 |
foaf:isPrimaryTopicOf | wikipedia-en:Helly_space |
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is foaf:primaryTopic of | wikipedia-en:Helly_space |