Foundations of Non-commutative Analysis: The Seonggil Preserving Limit Operator and Weyl Stress

Key Points

• This research aims to redefine the limit operator in calculus to retain infinitesimal topological information.
• Introduced the Seonggil Preserving Limit Operator (limS) within Rough Operator Algebra (ROA).
• Proved that the discarded infinitesimal results in a non-commutative residual torsion tensor representing Weyl stress.
• Analyzed the implications on the relationship between number theory and cosmological dynamics.
• Demonstrated that the infinitesimal component is a non-commutative residual torsion tensor (ϵS) rather than zero.
• Established that tensor-preserving operations provide an effective alternative to classical limits in analytic contexts.
• Showed a potential connection between analytic number theory and global cosmological dynamics.

Abstract