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Creators/Authors contains: "Bubenik, Peter"

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  1. ; ; ; ; ; ; (, Scientific Reports)
    Free, publicly-accessible full text available December 1, 2026
  2. (, Canadian Mathematical Bulletin)
    Abstract We give necessary and sufficient conditions for certain pushouts of topological spaces in the category of Čech’s closure spaces to agree with their pushout in the category of topological spaces. We prove that in these two categories, the constructions of cell complexes by a finite sequence of closed cell attachments, which attach arbitrarily many cells at a time, agree. Likewise, the constructions of CW complexes relative to a compactly generated weak Hausdorff space that attach only finitely many cells, also agree. On the other hand, we give examples showing that the constructions of finite-dimensional CW complexes, CW complexes of finite type, and relative CW complexes that attach only finitely many cells, need not agree. 
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    Free, publicly-accessible full text available June 20, 2026
  3. ; (, Journal of Pure and Applied Algebra)
    Free, publicly-accessible full text available February 1, 2026
  4. ; (, Journal of Applied and Computational Topology)
    Abstract. We develop persistent homology in the setting of filtrations of (Cˇech) closure spaces. Examples of filtrations of closure spaces include metric spaces, weighted graphs, weighted directed graphs, and filtrations of topological spaces. We use various products and intervals for closure spaces to obtain six homotopy theories, six cubical singular homology theories, and three simplicial singular homology theories. Applied to filtrations of closure spaces, these homology theories produce persistence modules. We extend the definition of Gromov-Hausdorff distance from metric spaces to filtrations of closure spaces and use it to prove that any persistence module obtained from a homotopy-invariant functor on closure spaces is stable. 
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  5. ; (, Computational Geometry)
    Full Text Available 
  6. ; (, ArXivorg)
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  7. ; (, Journal of Applied and Computational Topology)
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  8. ; (, Fields Institute communications)
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  9. ; ; (, 2021 IEEE International Conference on Big Data (Big Data))
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  10. ; ; ; ; ; ; (, Patterns)
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