Universal Covering: Basics

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Fundamental Groups

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

Sobolev Spaces and Unitary Groups

Explores Sobolev spaces, unitary groups, Laplacian properties, and translation groups in L^2.

Real Numbers: Sets and Operations

Explores the fundamental concepts of real numbers, including sets, operations, and properties like supremum and infimum.

Introduction to Real Numbers

Introduces the axiomatic structure of real numbers and their properties, including completeness and the Archimedean property.

Symmetries and Groups in Quantum Mechanics

Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.

Complex Numbers: Operations and Polar Form

Explores complex numbers, operations, absolute value, and polar form, along with the analysis and graphic representation of complex numbers.

Electromagnetic Problems: Well-Posedness and Convergence

Explores the well-posedness and convergence of electromagnetic problems, including continuity interpolation, Darcy's law, and surjectivity properties.

Universal Covering

Explores the concept of a universal cover of a topological space and the necessary conditions for a space to have one.

Real Numbers: Sets and Operations

Covers the fundamental concepts related to real numbers, including sets, notations, and operations.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.