Lectures related to Vector Spaces and Topology

Covers open balls in Euclidean spaces, their properties, and their significance in topology.

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

Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.

Discusses norms, distances, and the classification of open and closed sets in mathematical analysis.

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

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

Introduces the basics of real vector spaces, norms, and scalar products.

Explores orthogonality, scalar product, and orthonormal bases in vector spaces.

Explores polynomial operations, properties, and subspaces in vector spaces.

Explains the definition of Sobolew spaces and their main properties, focusing on weak denivelre.