A Calculus of Regions Respecting Both Measure and Topology.

Say that space is 'gunky' if every part of space has a proper part. Traditional theories of gunk, dating back to the work of Whitehead in the early part of last century, modeled space in the Boolean algebra of regular closed (or regular open) subsets of Euclidean space. More recently a complaint was...

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Publicado en:Journal of Philosophical Logic Vol. 48; no. 5; pp. 825 - 851
Autores principales: Lando, Tamar, Scott, Dana
Formato: Artículo
Publicado: Springer Nature Oct2019
Materias:
Acceso en línea:Ver este registro en EBSCOhost
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      dt: Oct2019
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        atl: A Calculus of Regions Respecting Both Measure and Topology.
      aug:
        au:
          Lando, Tamar
          Scott, Dana
        affil:
          Columbia University, 708 Philosophy Hall, 1150 Amsterdam Ave., Mail Code: 4971, 10027, New York, NY, USA
          University of California, Berkeley, 1149 Shattuck Avenue, 94707-2609, Berkeley, CA, USA
      su:
        Calculus
        Topology
        Lebesgue measure
        Borel subsets
        Boolean algebra
      sug:
        subj:
          Calculus
          Topology
          Lebesgue measure
          Borel subsets
          Boolean algebra
      keyword:
        Gunk
        Mereology
        Mereotopology
        Point-free space
        Regions
      ab: Say that space is 'gunky' if every part of space has a proper part. Traditional theories of gunk, dating back to the work of Whitehead in the early part of last century, modeled space in the Boolean algebra of regular closed (or regular open) subsets of Euclidean space. More recently a complaint was brought against that tradition in Arntzenius (2008) and Russell (2008): Lebesgue measure is not even finitely additive over the algebra, and there is no countably additive measure on the algebra. Arntzenius advocated modeling gunk in measure algebras instead—in particular, in the algebra of Borel subsets of Euclidean space, modulo sets of Lebesgue measure zero. But while this algebra carries a natural, countably additive measure, it has some unattractive topological features. In this paper, we show how to construct a model of gunk that has both nice rudimentary measure-theoretic and topological properties. We then show that in modeling gunk in this way we can distinguish between finite dimensions, and that nothing in lost in terms of our ability to identify points as locations in space.
      pubtype: Academic Journal
      doctype: Article
      src: R
    language: English
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