CORR
2011
Springer
13 years 2 months ago
2011
Springer
Given a function f : X → R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the exten...
COMPGEOM
2005
ACM
14 years 29 days ago
2005
ACM
The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the p...
COMPGEOM
2009
ACM
14 years 5 months ago
2009
ACM
Topological persistence has proven to be a key concept for the study of real-valued functions defined over topological spaces. Its validity relies on the fundamental property tha...