Norms and Valuations on Fields

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Related lectures (30)

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

Extension of Fields: Norm and Valuation

Covers the extension of fields, defining the norm of an element from one field to another, and introducing the p-adic valuation.

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.

Real Estate Investment: Valuation and Analysis

Explores real estate investment valuation, construction costs, and property pricing factors.

Norm Extension in Finite Fields

Covers the uniqueness of norm extension in finite fields and the construction of norms on finite extensions of Qp.

Algebraic Fields: Transcendence Degree

Explores transcendence degree in algebraic fields and classical analytic functions.

Metric Spaces: Norms and Distances

Explores norms, distances, scalar products, and norm convergence in metric spaces.

Metric Spaces: Topology and Continuity

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

Definition of Sobolew Spaces

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

P-adic Expansion and Hensel's Lemma

Covers the p-adic expansion theorem and Hensel's Lemma in Qp.