Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Concept

Locally simply connected space

Related lectures (20)

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.

Universal Covering: Basics

Covers the concept of universal covering and its properties, including examples and monodromy action.

Hyperbolic Geometry

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Vector Fields and Potentials

Explores vector fields, potentials, and their relationship, focusing on necessary and sufficient conditions.

Green's Theorem: Domain Analysis

Explores Green's Theorem application in domain analysis and potential functions.

Fundamental Groups

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

Base B for X: Connected Sets and Open Bases

Explores the concept of a base B for a topological space X and the properties of connected sets and open bases.

Real Functions: Definitions and Theorems

Explores real functions, covering continuity, supremum, infimum, maximum, minimum, compact and connected sets, and the intermediate value theorem.

Analysis III: Third Class

Covers the correction of the simple curve definition and the importance of orientation in mathematical analysis.

Electromagnetic Problems: Well-Posedness and Convergence Log in to Mediaspace to watch this video

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

Spectrum of Hyperbolic Surfaces Log in to Mediaspace to watch this video

Explores the spectrum of hyperbolic surfaces, discussing thin C-principle, grad, normalized functions, minimum volume, and embedding properties.

Curvilinear Integrals: Fundamentals Log in to Mediaspace to watch this video

Covers the fundamentals of curvilinear integrals and their calculations, emphasizing the importance of orientation in integrals.

Properties of Limits Log in to Mediaspace to watch this video

Covers the properties of limits and functions of multiple variables.

Green-Riemann Formula: Curvilinear Integrals Log in to Mediaspace to watch this video

Covers the Green-Riemann formula, connectedness by arcs, parametrization of curves, and open simply connected domains in the Oxy plane.

Advanced Analysis II: Matrix Diagonalization Log in to Mediaspace to watch this video

Covers matrix diagonalization, compact sets, continuity of functions, and the Mandelbrot set.

Mayer-Vietoris Sequence Log in to Mediaspace to watch this video

Explores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.

Curvilinear Integrals, Conservative Fields, and Green's Theorem Log in to Mediaspace to watch this video

Covers curvilinear integrals, conservative fields, and Green's Theorem with examples.

Advanced Analysis II: Eigenvalues and Compact Sets Log in to Mediaspace to watch this video

Covers the reconstruction of a table using diagonal matrices and explores extreme values and set definitions.

Fourier Transform: Solution of Mock Exam Log in to Mediaspace to watch this video

Covers the solution of a mock exam for Analysis III, focusing on Fourier coefficients and vector fields.

Curvilinear Integrals and Conservative Fields Log in to Mediaspace to watch this video

Explores curvilinear integrals, conservative fields, and their implications in various contexts.