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Completion of the Proof of the Arzela-Ascoli Theorem and Introduction to Montels Theorem, by T.E. Venkata Balaji

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The Weight Two Modular Form Assumes Real Values on the Imaginary Axis in the Upper Half-Plane, by T.E. Venkata Balaji

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Normal Sequential Compactness, Normal Uniform Boundedness and Montel’s & Marty’s Theorems at Infinity, by T.E. Venkata Balaji

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Proofs of Two Avatars of the Residue Theorem for the Extended Complex Plane and Applications of the Residue at Infinity, by T.E. Venkata Balaji

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A Region in the Upper Half-Plane Meeting each Unimodular Orbit Exactly once, by T.E. Venkata Balaji

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Analytic Continuability along Paths: Dependence on the Initial Function and on the Path-First Version of the Monodromy Theorem, by T.E. Venkata Balaji

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A Fundamental Region in the Upper Half-Plane for the Elliptic Modular J-Invariant, by T.E. Venkata Balaji

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The Birth of Local Rings in Geometry and in Algebra, by T.E. Venkata Balaji

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Completion of the Construction of the Universal Covering: The Fundamental Group of the Base as the Deck Transformation Group, by T.E. Venkata Balaji

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Completion of Proof of the Riemann Mapping Theorem, by T.E. Venkata Balaji

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A Riemann Surface Structure on a Torus, by T.E. Venkata Balaji

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Royden’s Theorem on Normality Based on Growth of Derivatives, by T.E. Venkata Balaji

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The Idea of a Direct Analytic Continuation Or an Analytic Extension, by T.E. Venkata Balaji

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Reducing Existence of Riemann Mappings to Hyperbolic Geometry of Sub-Domains of the Unit Disc, by T.E. Venkata Balaji

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Hurwitz’s Theorem for Normal Limits of Meromorphic Functions in the Spherical Metric, by T.E. Venkata Balaji

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Morphisms into an Affine Correspond to K-Algebra Homomorphisms from its Coordinate Ring of Functions, by T.E. Venkata Balaji

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Schottky’s Theorem: Uniform Boundedness from a Point to a Neighbourhood & Problem Solving Session, by T.E. Venkata Balaji

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Simple Examples of Riemann Surfaces, by T.E. Venkata Balaji

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Hyperbolic Geodesics for the Hyperbolic Metric on the Unit Disc, by T.E. Venkata Balaji

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The Weight Two Modular Form Decays Exponentially in a Neighbourhood of Infinity, by T.E. Venkata Balaji

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Maximal Domains of Direct and Indirect Analytic Continuation: Secondversion of the Monodromy Theorem, by T.E. Venkata Balaji

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Completion of Proof of Hurwitz’s Theorem for Normal Limits of Analytic Functions in the Spherical Metric, by T.E. Venkata Balaji

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Completion of the Construction of the Universal Covering: Universality of the Universal Covering, by T.E. Venkata Balaji

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Irreducibility in the Zariski Topology, by T.E. Venkata Balaji

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Deducing the Second (Simply Connected) Version of the Monodromy Theorem from the first (Homotopy) Version, by T.E. Venkata Balaji

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F (Z,W) =0 is Naturally a Riemann Surface, by T.E. Venkata Balaji

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Morera’s Theorem at Infinity, Infinity as a Pole and Behaviour at Infinity of Rational and Meromorphic Functions, by T.E. Venkata Balaji

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Why Local Rings Provide Calculus without Limits for Algebraic Geometry Pun Intended!, by T.E. Venkata Balaji

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Geometric Hypersurfaces are Precisely Algebraic Hypersurfaces, by T.E. Venkata Balaji

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Capturing an Affine Variety Topologically from the Maximal Spectrum of its Ring of Functions, by T.E. Venkata Balaji

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