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Lecture
Universal Covering: Basics
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Related lectures (32)
Fundamental Groups
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
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
MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers
MOOC: Analysis I
Introduces the axiomatic structure of real numbers and their properties, including completeness and the Archimedean property.
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.
Real Analysis Basics
Covers the basics of real analysis, including limits, sequences, and continuous functions.
Real Numbers: Sets and Operations
Covers the basics of real numbers and set theory, including subsets, intersections, unions, and set operations.
Real Numbers Sequences
Explores real number sequences, convergence, limits, boundedness, and monotonicity.
Real Number Sequences: Cauchy Sequences
MOOC: Analysis I
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Discusses Cauchy sequences, sub-sequences, and numerical series with parameters.
Prelude: Linking Mathematics and Course Content
MOOC: Warm-up for EPFL
MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers
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Introduces the course content by linking familiar mathematics with upcoming topics.
Important Property of Archimedean Bodies
MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers
MOOC: Analysis I
Covers the Archimedean property and the proposition for all x in a set, there exists a positive real number n such that n*x is greater than y.
Real Numbers: Absolute Value and Density
Covers absolute value, density of rationals, and real line topology.
Roots of Real Numbers
Explores the properties and applications of roots of real numbers through practical examples.
Real Numbers: Decimal Notation
Explores the concept of real numbers through decimal notation and fraction representation.
Limits of Sequences
Explores the concept of limits of sequences and their convergence towards infinity or negative infinity.
Bounding the Poisson bracket invariant on surfaces
Covers the concept of bounding the Poisson bracket invariant on surfaces, exploring joint work with A. Logunov and S. Tanny.
Sobolev Spaces and Unitary Groups
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Explores Sobolev spaces, unitary groups, Laplacian properties, and translation groups in L^2.
Complex Numbers: Operations and Polar Form
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Explores complex numbers, operations, absolute value, and polar form, along with the analysis and graphic representation of complex numbers.
Universal Covering
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Explores the concept of a universal cover of a topological space and the necessary conditions for a space to have one.
Electromagnetic Problems: Well-Posedness and Convergence
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Explores the well-posedness and convergence of electromagnetic problems, including continuity interpolation, Darcy's law, and surjectivity properties.
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