Explains the properties of subsets of real numbers, including Supremum, Infimum, intervals, open sets, and closed sets.
Covers strings, countable sets, cardinality, and the concept of countability, exploring the countability of various sets and Cantor diagonalization.
Explores intervals in real numbers, including open and closed intervals, periodic decimals, and irrational numbers.
Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Covers the concept of separable L^2 spaces, demonstrating properties and providing examples.
Covers the properties of real numbers, focusing on the total order and completeness, including the Archimedean property and the concepts of supremum and infimum.
