  Topological data analysis (TDA) is a rising field in the intersection of
mathematics, statistics, and computer science/data science. The cornerstone of
TDA is persistent homology, which produces a summary of topological information
called a persistence diagram. To utilize machine and deep learning methods on
persistence diagrams, These diagrams are further summarized by transforming
them into functions. In this paper we investigate the stability and injectivity
of a class of smooth, one-dimensional functional summaries called Gaussian
persistence curves.
