Metric Spaces: Norms and Distances

This lecture covers the definition of norms and distances in a vector space, exploring the equivalence of different norms, the concept of metric spaces, and the properties of distances and metrics. It also delves into scalar products, the Cauchy-Schwarz inequality, and the equivalence of norms induced by scalar products. The lecture concludes with discussions on norm convergence and the independence of convergence on the choice of norm.