Concept

Metrizable topological vector space

Related lectures (32)

Manifolds: Charts and Compatibility

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Properties of Weak Derivatives

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

Categorical Perspective: Group Actions

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

Functional Analysis and Distribution Theory

Introduces functional analysis, distribution theory, topological vector spaces, and linear operators, emphasizing their importance in engineering applications.

Dimension Theory: Topological Space and Closed Subsets

Explores dimension theory in topological spaces and closed subsets, including height interpretation and additivity.

School Product: Geometric Properties

Covers the school product and geometric properties of vectors in space.

Approximation by Smooth Functions

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Lifting Criterion

Explores the lifting criterion for maps between path-connected and locally path-connected spaces.

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.

Interpolation Spaces

Explores interpolation spaces between Banach spaces and real interpolation spaces.

Dimension theory of rings

Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Metric Spaces: Topology and Continuity

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Sheaves: Hartshorne I.1

Covers the concept of sheaves, emphasizing the unique determination of functions by local data and the importance of direct limits.

Orthogonality, Triangle Inequality, Pythagorean Theorem

Explores orthogonality, triangle inequality, and the Pythagorean theorem in vector spaces.

Modular curves: Riemann surfaces and transition maps

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

Orthogonal Projection: Geometrical Interpretation

Explains finding the closest point on a plane using orthogonal projection.

Quantum Physics I

Covers state vectors, Dirac notation, eigen-kets, and Hermitian operators in quantum physics.

Norme, Cauchy-Schwarz Inequality

Covers the definition of norm, distance between vectors, and Cauchy-Schwarz inequality.

Advanced-analysis-ii

Explores advanced analysis topics, including Cauchy sequences, Banach spaces, and the Cauchy-Lipschitz theorem.