The Theory of Persistence -- Articles M1-M5: Mathematical Foundations

Key Points

• This series aims to solidify the mathematical underpinnings of the Theory of Persistence by providing rigorous definitions and frameworks.
• Published five articles presenting mathematical theories and principles related to Persistence Theory.
• Included companion scripts for verifying mathematical concepts and findings.
• Emphasized the relationship between topological data analysis and Persistence Theory.
• Clarified the mathematical definitions relevant to Persistence Theory and its applications.
• Provided tools for verifying the theoretical aspects of Persistence Theory through scripts.
• Set the stage for future applications and research grounded in solid mathematical foundations.