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Using the notion of order convergent nets, we develop an order-theoreticapproach to differentiable functions on Archimedean complex $\Phi$-algebras.Most notably, we improve the Cauchy-Hadamard formulas for universally completecomplex vector lattices given by both authors in a previous paper in order toprove that analytic functions are holomorphic in this abstract setting.

Differentiable, Holomorphic, and Analytic Functions on Complex $\Phi$-Algebras