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Complete topological vector space
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Related lectures (31)
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Spatial Topological Queries
Explores topology, test functions, and space operators for spatial queries.
Approximation by Smooth Functions
Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.
Dimension Theory: Topological Space and Closed Subsets
Explores dimension theory in topological spaces and closed subsets, including height interpretation and additivity.
Functional Analysis and Distribution Theory
Introduces functional analysis, distribution theory, topological vector spaces, and linear operators, emphasizing their importance in engineering applications.
Functional Analysis: Banach and Hilbert Spaces
Covers Banach and Hilbert spaces, separability, norm, continuity, and functional analysis.
Group Actions: Examples
Showcases examples of group actions on vector spaces and topological spaces.
Group Actions and Fundamental Groups
Delves into group actions, coverings, fundamental groups, and homomorphisms in topological spaces.
Lifting Criterion
Explores the lifting criterion for maps between path-connected and locally path-connected spaces.
Kernel, Image and Linear Maps
Explains kernel, image, and linear maps, illustrating concepts with examples.
Vector Spaces: Bases and Dimension
Explains bases and dimension in vector spaces, covering generative and free families, isomorphism, and key theorems.
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.
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