Real and complex analysis
Book
Formal Antecedent
Foundations and Logic
Citation
Rudin, Walter. (1987). Real and complex analysis. McGraw-Hill.
Why this reference is included
Rudin’s Real and complex analysis (1987), published by McGraw-Hill, sits in the program’s reference corpus as a standing technical source. Cited 5 times across Book II (Categorical Holomorphy), Part 0, Chapter The Boundary-First Paradigm; Book II (Categorical Holomorphy), Part 0, Chapter Roadmap and Inverted Dependency; Book II (Categorical Holomorphy), Part 6, Chapter Laurent Series and Residues, and in 2 further chapters.
Cited in
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Book II — Categorical Holomorphy Part 0Chapter The Boundary-First Paradigm
Classical SCV: Interior to Boundary In the orthodox tradition of several complex variables, the interior comes first
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Book II — Categorical Holomorphy Part 0Chapter Roadmap and Inverted Dependency
cylinder compat.) , continuity & topology & (Part III: unique topology making NF continuous) , topology & geometry & (Part IV: ultrametric ⇒ Tarski axioms) , geometry & transcendentals & (Part V: π, e, j, ι_τ from earned geometry) , In orthodox analysis the arrows run in the opposite direction: transcendentals (ℝ assumed) ⇒ geometry (ℝ^n) ⇒ topology (open sets) ⇒ continuity (-δ) ⇒ holomorphy (Cauchy–Riemann )
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Book II — Categorical Holomorphy Part 6Chapter Laurent Series and Residues
The Residue Theorem The classical residue theorem states _γ f(z) dz = 2π i Res_z_k(f)
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Book II — Categorical Holomorphy Part 9Chapter Hartogs Extension in H_τ
The classical proof relies on the Cauchy integral or the ∂-equation — tools that are not available in Category τ
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Book II — Categorical Holomorphy Part 9Chapter Liouville Categorical Dodge and Categoricity
The classical Liouville theorem states: f is constant