# P-persistent homology of finite topological spaces

Published in *Rendiconti Sem. Mat. Univ. Pol. Torino*, 2015

Vaccarino, F., Patania, A., & Petri, G. (2017). *Rendiconti Sem. Mat. Univ. Pol. Torino*. Vol. 74, 1. 27 - 45.

Let P be a finite partially ordered set, briefly a finite poset. We will show that for any P-persistent object X in the category of finite topolog- ical spaces, there is a P− weighted graph, whose clique complex has the same P-persistent homology as X. ArXiv pre-print