Study of topological concepts in metric spaces (neighborhoods, open sets, closed sets, closed sets, subspaces, separable metric spaces), sequences in metric spaces, complete metric spaces, continuous functions and homeomorphisms in metric spaces, compact metric spaces (sets compact, finite intersection properties, sequential compact ), Baire categories, function sequences (convergence of function sequences, Ascoli-Arzela Theorem), topological spaces (basic concepts in topological spaces, subspaces, bases and subbases ), measurable sets, properties properties of measurable sets, Lebesgue measures, immeasurable sets, measurable functions, Lebesgue Integrals, general measures and integrals, and classical Banach Spaces. Lectures begin with an explanation of concepts and principles, assignments and discussions with students, as well as presentations using ICT with an assessment system including assignments (30%), participation (20%), mid-semester assessment (20%) and final semester assessment (30%).
