User:Anghel/Projects
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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