Real Functions: Definitions and Theorems

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Optimal Transport: Analysis and Proofs

Explores optimal transport analysis and proofs, emphasizing weak convergence and compactness.

Compact Sets and Extreme Values

Explores compact sets, extreme values, and function theorems on bounded sets.

Real Analysis: Functions and Limits

Covers the basics of real analysis, including functions, limits, and max/min functions.

Real Functions: Composition and Limits

Explores real functions, composition, and limits, including algebraic operations and sequence characterization.

Uniqueness of Solutions: Cauchy-Lipschitz Theorem

Covers the uniqueness of solutions in differential equations, focusing on the Cauchy-Lipschitz theorem and its implications for local and global solutions.

Sequences and Convergence: Understanding Mathematical Foundations

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Convergence and Limits in Real Numbers

Explains convergence, limits, bounded sequences, and the Bolzano-Weierstrass theorem in real numbers.

Uniqueness of Solutions: Cauchy-Lipschitz Theorem

Covers the uniqueness of solutions in differential equations, focusing on the Cauchy-Lipschitz theorem and its implications for local and global solutions.

Continuous Functions on Compact Sets

Explores continuous functions on compact sets, discussing boundedness and extremum values.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.