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

(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 ...
• #### Equivalent Euclidean Data Complexes ﻿

(Master thesis, 2021-06-01)
Euclidean data complexes are simplicial complexes that have been constructed from a point cloud in Euclidean space. Two of the most important examples of such complexes are the Čech and Alpha complex. In this thesis, we ...