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Analyse II: Theorems on Continuous Functions and Extremums

Covers the theorems on continuous functions and extremums in compact sets.

Properties of Coatings

Covers the properties of coatings, including trivializing opens and automorphisms.

Advanced analysis II

Covers Jordan-measurable sets, Riemann-integrability, and function continuity on compact sets.

Advanced Analysis I: Continuous Functions on Compact Sets

Explores the necessity of uniform continuity for continuous functions on compact sets.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Cauchy-Lipschitz Theorem

Explores the Cauchy-Lipschitz theorem for ODE solutions and linear transformations.

Lattices: Theory and Applications

Explores the theory of lattices, their properties, and applications in different mathematical contexts, emphasizing local-global principles.

Continuous Functions on Compact Sets

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

Bolzano-Weierstrass Theorem: Sequential Compactness in Hilbert Spaces

Explores the Bolzano-Weierstrass theorem in Hilbert spaces, showcasing sequential compactness and the construction of converging subsequences.

Quotients in Abelian Groups

Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.