7 citations · 7 across the 6 of their papers we have counts for
5 papers · 1 filter
A continuum of Künneth theorems for persistence modules
Nikola Milićević
We develop new aspects of the homological algebra theory for persistence modules, in both the one-parameter and multi-parameter settings. For a poset and an order preserving ma…
A McCord-type theorem for pseudotopological spaces and directed graphs
Nikola Milićević, Nicholas A. Scoville
We construct weak homotopy equivalences between the geometric realizations of directed Vietoris-Rips complexes and their underlying directed graphs, seen as pseudotopological space…
Singular homology of roots of unity
Nikola Milićević
We extend some basic results from the singular homology theory of topological spaces to the setting of Čech's closure spaces. We prove analogues of the excision and Mayer-Vietoris…
Eilenberg-Steenrod homology and cohomology theories for Čech's closure spaces
Peter Bubenik, Nikola Milićević
We generalize some of the fundamental results of algebraic topology from topological spaces to Čech's closure spaces, also known as pretopological spaces. Using simplicial sets and…
Homotopy, homology, and persistent homology using closure spaces
Peter Bubenik, Nikola Milićević
We develop persistent homology in the setting of filtrations of (Cech) closure spaces. Examples of filtrations of closure spaces include metric spaces, weighted graphs, weighted di…