Browsing Bergen Open Research Archive by Author "Salbu, Lars Moberg"

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    • Determining homology of an unknown space from a sample 

      Brun, Morten; Garcia Pascual, Belen; Salbu, Lars Moberg (Journal article; Peer reviewed, 2023)
      The homology of an unknown subspace of Euclidean space can be determined from the intrinsic Čech complex of a sample of points in the subspace, without reference to the ambient Euclidean space. More precisely, given a ...

    • Dowker’s Theorem by Simplicial Sets and a Category of 0-Interleavings 

      Salbu, Lars Moberg (Master thesis, 2019-06-21)
      In this thesis we look at an alternative proof of Dowker’s theorem [4] using simplical sets. We prove the strongest version of the theorem [3], which can be applied to persistence homology in the sense that every nested ...

    • The Rectangle Complex of a Relation 

      Brun, Morten; Salbu, Lars Moberg (Journal article; Peer reviewed, 2023)
      We construct a simplicial complex, the rectangle complex of a relation R, and show that it is homotopy equivalent to the Dowker complex of . This results in a short and conceptual proof of functorial versions of Dowker’s ...