Banach manifold structure and infinite-dimensional analysis for causal fermion systems

A mathematical framework is developed for the analysis of causal fermion systems in infinite-dimensional setting. It shown that regular spacetime point operators form a Banach manifold endowed with canonical Fr\'echet-smooth Riemannian metric. The so-called expedient differential calculus introduced purpose treating derivatives functions on spaces which are differentiable only certain directions. chain rule proven H\"older continuous subspaces. These results made applicable to by proving Lagrangian continuous. Moreover, continuity analyzed integrated Lagrangian.