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Concept

Connected space

Related lectures (31)

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.

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.

Networked Control Systems: Consensus Algorithms in Digraphs

Explores consensus algorithms in digraphs, focusing on scenarios where the digraph is not strongly connected.

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.

Separation Criterion in Recollement

Focuses on a criterion for separability in recollement, demonstrating iron properties and applications in various cases.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Fundamental Groups

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

Surfaces: The Torus

Explores the definition of surfaces, focusing on the torus and its construction through various examples and morphic images.

Open Mapping Theorem

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Hyperbolic Geometry

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

Wedge: Family of Spaces

Explores the concept of a wedge of spaces and explicit parainization.

Connected Components

Explores connected components in a decked space and the well-defined application of functions.

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.

Modular curves: Riemann surfaces and transition maps

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Local structure of totally disconnected locally compact groups III

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Endomorphisms and automorphisms of totally disconnected locally compact groups I

Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.

Vector Fields and Potentials

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

Networked Control Systems: Strongly Connected Components and Condensation Digraphs

Explores strongly connected components and condensation digraphs in networked control systems, demonstrating their practical implications.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Green's Theorem: Domain Analysis

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