Sillabus:

Sequence of real-valued functions: pointwise convergence and uniform convergence of a sequence of real-valued functions and their applications.

Metric spaces: the definition of metric spaces, neighborhoods, interior points, limit points, closure points, boundary points, open sets, closure, closed sets, subspaces, separability, sequences in metric spaces, complete metric spaces, continuity of functions on metric spaces, compactness, Heine-Borel Theorem.