Necessary Conditions for Discontinuities of Multidimensional Size Functions
Andrea Cerri, Patrizio Frosini
TL;DR
This paper explores the conditions under which discontinuities occur in multidimensional size functions, linking these points to pseudocritical or special values of the measuring functions, advancing understanding in topological persistence.
Contribution
It provides new theoretical results connecting discontinuities in size functions to specific critical values, enhancing the mathematical framework of multidimensional topological persistence.
Findings
Discontinuities are linked to pseudocritical values.
Discontinuity points relate to special values of measuring functions.
Provides conditions for discontinuities in multidimensional size functions.
Abstract
Some new results about multidimensional Topological Persistence are presented, proving that the discontinuity points of a k-dimensional size function are necessarily related to the pseudocritical or special values of the associated measuring function.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory