User:Anghel/Projects

Projects

• Goursat's Integral Lemma -tidy ,Tao notation, add new picture
• Continuous Functions on Compact Space form Banach Space - add proof
• Elements of Module with Equal Images under Linear Transformations form Submodule - prove without Submodule Test
• Directed Smooth Curve Relation is Equivalence - Generalizes to $\R$ without problems.
• Definition:Piecewise Continuously Differentiable Function - add complex definition, add closed interval at Definition:Complex-Differentiable Function
• Path Homotopy is Equivalence Relation - add proof, special case of relative homotopy
• Definition:Adjoint (Norm Theory) - add definition from Meise & Vogt
• Definition:Neighborhood (Complex Analysis) - merge with Definition:Open Complex Disk, and merge the disks with the balls, match definition with Definition:Neighborhood (Topology), cite AMS: Joshua Bowman
• Derivative of Complex Composite Function - correct proof
• Triangle Inequality/Vectors in Euclidean Space - proof from Cauchy-Schwarz, and refactor
• Angle Between Non-Zero Vectors Always Defined - add link to above, correct Definition:Angle Between Vectors
• Contour Integration by Substitution - add simply connected domain => primitive
• Weierstrass M-Test - add complex case
• Epsilon-Function Differentiability Condition/Complex Case - add claim of continuous differentiability
• Definition:Path (Topology) - add page Closed Real Intervals are Homeomorphic
• Norm is Continuous - merge
• Definition:Unit Ball - merge with Definition:Closed Unit Ball
• Definition:Compact Space/Real Analysis - add equivalence theorem
• Equivalence of Definitions of Boundary - construct proof
• Three Regular Tessellations/Squares - add proof
• Heine-Borel Theorem/Real Line - explain example
• Charles Babbage's Conjecture - counterexample ^2
• Absolutely Convergent Generalized Sum Converges - simple clarification
• Inverse of Matrix is Scalar Product of Adjugate by Reciprocal of Determinant - add proof based on Matrix Product with Adjugate Matrix
• Definition:Contour/Simple - add example link to parameterization of $\map {N_1} 0$, to show simple and closed contour.
• Definition:Measure (Measure Theory)
• Inverse Function Theorem - proof from Wikipedia
• Separated Sets are Clopen in Union
• Uniform Convergence is Hereditary - add proof?
• Equivalence of Definitions of Boundary - create proof
• All Normal Vectors of Simple Closed Contour Cannot Point into Interior/Lemma 1 - Borsuk Lemma, combined with line between vectors, Also, Corner Smoothening Lemma.
• Arzelà-Ascoli Theorem
• Carathéodory's Theorem (Measure Theory) - add proof
• Definition:Pi - check up on various theorems about the periodicity of pi
• Definition:Definite Integral - add proofs and correct various subpages, add Stieltjes definition and historical notes (from Mål- og Integralteori)
• Note on Definition:Quotient Mapping
• Definition:Rotation (Geometry) - correct definition, add matrices proof