Matches in SemOpenAlex for { <https://semopenalex.org/work/W2015581837> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W2015581837 endingPage "59" @default.
- W2015581837 startingPage "1" @default.
- W2015581837 abstract "The Hahn-Banach theorem is one of many fundamental results in functional analysis whose usefulness is diminished by their proof depending upon an application of the Axiom of Choice. The objection raised in this regard is not philosophical, but purely practical. When the existence of a functional has been established by this non-constructive means, the arbitrariness introduced restricts the information which can be extracted, impeding the discussion of points such as whether the functional can be shown to exist continuously with respect to a parameter [ 1, 15, 201, or equivariantly with respect to a group action [2, 333. This paper is concerned with outlining, starting from ideas which are already established, a context and a technique which allow the effects of this dependence on the Axiom of Choice to be avoided, reformulating the Hahn-Banach theorem in a way which may be applied equally to questions of continuity and of equivariance, to yield the information which is traditionally intended when applying the Hahn-Banach theorem. Before introducing the constructive context in which these ideas will be developed, consider the situations already mentioned, in which the arbitrariness of the existence of a functional established by the Axiom of Choice presents difficulties which need to be resolved. Firstly, take that of continuity in a parameter, which may be stated more precisely in the following way: consider a bundle B of seminormed spaces on a topological space X, together with a continuous mapping" @default.
- W2015581837 created "2016-06-24" @default.
- W2015581837 creator A5019238697 @default.
- W2015581837 creator A5048052873 @default.
- W2015581837 date "1991-09-01" @default.
- W2015581837 modified "2023-10-01" @default.
- W2015581837 title "A globalization of the Hahn-Banach theorem" @default.
- W2015581837 cites W1602062035 @default.
- W2015581837 cites W1978865426 @default.
- W2015581837 cites W2012934034 @default.
- W2015581837 cites W2042984937 @default.
- W2015581837 cites W2046209511 @default.
- W2015581837 cites W2058996432 @default.
- W2015581837 cites W2059529852 @default.
- W2015581837 cites W2075513489 @default.
- W2015581837 cites W2090967105 @default.
- W2015581837 cites W242489048 @default.
- W2015581837 cites W2583712585 @default.
- W2015581837 cites W4212886760 @default.
- W2015581837 cites W4213060855 @default.
- W2015581837 doi "https://doi.org/10.1016/0001-8708(91)90082-i" @default.
- W2015581837 hasPublicationYear "1991" @default.
- W2015581837 type Work @default.
- W2015581837 sameAs 2015581837 @default.
- W2015581837 citedByCount "34" @default.
- W2015581837 countsByYear W20155818372014 @default.
- W2015581837 countsByYear W20155818372016 @default.
- W2015581837 countsByYear W20155818372017 @default.
- W2015581837 countsByYear W20155818372018 @default.
- W2015581837 countsByYear W20155818372019 @default.
- W2015581837 countsByYear W20155818372020 @default.
- W2015581837 countsByYear W20155818372021 @default.
- W2015581837 countsByYear W20155818372022 @default.
- W2015581837 crossrefType "journal-article" @default.
- W2015581837 hasAuthorship W2015581837A5019238697 @default.
- W2015581837 hasAuthorship W2015581837A5048052873 @default.
- W2015581837 hasBestOaLocation W20155818371 @default.
- W2015581837 hasConcept C132954091 @default.
- W2015581837 hasConcept C136119220 @default.
- W2015581837 hasConcept C162324750 @default.
- W2015581837 hasConcept C172294467 @default.
- W2015581837 hasConcept C184908153 @default.
- W2015581837 hasConcept C202444582 @default.
- W2015581837 hasConcept C2119116 @default.
- W2015581837 hasConcept C33923547 @default.
- W2015581837 hasConcept C34447519 @default.
- W2015581837 hasConceptScore W2015581837C132954091 @default.
- W2015581837 hasConceptScore W2015581837C136119220 @default.
- W2015581837 hasConceptScore W2015581837C162324750 @default.
- W2015581837 hasConceptScore W2015581837C172294467 @default.
- W2015581837 hasConceptScore W2015581837C184908153 @default.
- W2015581837 hasConceptScore W2015581837C202444582 @default.
- W2015581837 hasConceptScore W2015581837C2119116 @default.
- W2015581837 hasConceptScore W2015581837C33923547 @default.
- W2015581837 hasConceptScore W2015581837C34447519 @default.
- W2015581837 hasIssue "1" @default.
- W2015581837 hasLocation W20155818371 @default.
- W2015581837 hasOpenAccess W2015581837 @default.
- W2015581837 hasPrimaryLocation W20155818371 @default.
- W2015581837 hasRelatedWork W1990278393 @default.
- W2015581837 hasRelatedWork W2008708286 @default.
- W2015581837 hasRelatedWork W2023548740 @default.
- W2015581837 hasRelatedWork W2036047225 @default.
- W2015581837 hasRelatedWork W2125932543 @default.
- W2015581837 hasRelatedWork W2318045364 @default.
- W2015581837 hasRelatedWork W2350748817 @default.
- W2015581837 hasRelatedWork W2782566858 @default.
- W2015581837 hasRelatedWork W2809393823 @default.
- W2015581837 hasRelatedWork W4245147957 @default.
- W2015581837 hasVolume "89" @default.
- W2015581837 isParatext "false" @default.
- W2015581837 isRetracted "false" @default.
- W2015581837 magId "2015581837" @default.
- W2015581837 workType "article" @default.