Metric and Topological Spaces

Metric spaces, open and closed sets. Euclidean spaces, normed linear spaces, examples of different normed linear spaces, sequence spaces. Completeness, Baire category Theorem. Compactness, characterization of compact spaces. Product spaces, Tychonoff’s theorem. Continuous functions, equicontinuous families, Arzela-Ascolli Theorem. Connectedness, path connectedness. Functions of several variables, Inverse function theorem, Implicit function theorem.