title: Spectrum of a separable Dynkin algebra and topology on it
metadata.name: dc.contributor.author
metadata.value: Vallander, Sergey S.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-09-18T11:22:46Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-09-18T11:22:46Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vallander S. S. Spectrum of a separable Dynkin algebra and topology on it. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 3, pp. 351–355.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.301
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/14880
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: We continue a preparation to the construction of generalized axiomatics of probability theory,
  begined in previous papers of author. Our approach is based on the investigation of set
  systems more general than usual set algebras and their Boolean versions. We name them
  Dynkin algebras. The spectrum of separable Dynkin algebra and appropriate Grothendieck
  topology on it are introduced. Separable Dynkin algebras constitute a natural class of a
  abstract Dynkin algebras defined by author previously. A structural result was received in
  this mentioned paper: every separable Dynkin algebra is a union of its maximal Boolean
  subalgebras. In this paper, we define, basing on this result, the spectrum of a separable
  Dynkin algebra and an appropriate Grothendieck topology on it. The corresponding constructions
  are similar to the construction of the simple spectrum of a commutative ring and
  that of the Zariski topology on it. The analogy here is incomplete: Zariski topology makes
  the spectrum of a commutative ring to be a usual topological space while Grothendieck
  topology, which is not a topology in usual sense, transforms the spectrum of a Dynkin
  algebra into a more abstract object (site or situs via Grothendieck). This is sufficient for
  our aims.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 5(63); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: separable Dynkin algebras
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: spectrum of a separable Dynkin algebra
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Grothendieck topology on spectrum
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Spectrum of a separable Dynkin algebra and topology on it
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 01-Vallander.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/14880/1/01-Vallander.pdf
resources.format: Adobe PDF
resources.size: 255,2 kB