ON EQUIVALENCE RELATIONS GENERATED BY SCHAUDER BASES.
In this article, a notion of Schauder equivalence relation ℝℕ/L is introduced, where L is a linear subspace of ℝℕ and the unit vectors form a Schauder basis of L. The main theorem is to show that the following conditions are equivalent:(1) the unit vector basis is boundedly complete;(2) L is a Fσ in...
| Publicado en: | Journal of Symbolic Logic Vol. 82; no. 4; pp. 1459 - 1482 |
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| Formato: | Artículo |
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Cambridge University Press
Dec2017
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=127197711&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 127197711 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00224812 3TY jtl: Journal of Symbolic Logic issn: 00224812 maglogo: N pubinfo: dt: Dec2017 vid: 82 iid: 4 pid: 15979 pub: Cambridge University Press artinfo: ui: 127197711 10.1017/jsl.2017.67 ppf: 1459 ppct: 23 formats: tig: atl: ON EQUIVALENCE RELATIONS GENERATED BY SCHAUDER BASES. aug: au: DING, LONGYUN affil: SCHOOL OF MATHEMATICAL SCIENCES AND LPMC NANKAI UNIVERSITY TIANJIN 300071, P.R. CHINA su: Mathematical equivalence Schauder bases Functional analysis Model theory Algorithmic randomness Applied mathematics sug: subj: Mathematical equivalence Schauder bases Functional analysis Model theory Algorithmic randomness Applied mathematics keyword: 46B15 46B45 Borel reduction equivalence relation Primary 03E15 Schauder basis ab: In this article, a notion of Schauder equivalence relation ℝℕ/L is introduced, where L is a linear subspace of ℝℕ and the unit vectors form a Schauder basis of L. The main theorem is to show that the following conditions are equivalent:(1) the unit vector basis is boundedly complete;(2) L is a Fσ in ℝℕ;(3) ℝℕ/L is Borel reducible to ℓ∞.We show that any Schauder equivalence relation generalized by a basis of ℓ2 is Borel bireducible to ℝℕ/ℓ2 itself, but it is not true for bases of c0 or ℓ1. Furthermore, among all Schauder equivalence relations generated by sequences in c0, we find the minimum and the maximum elements with respect to Borel reducibility. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2017 holdings: @attributes: islocal: N |
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