CORR
2011
Springer
13 years 3 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 1 months 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 6 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...