MAT 355 - Introduction to Topology

Course Objectives

Teaching basic concepts of metric spaces and abstract topological spaces to students in mathematics Engineering.

Course Description

Metric spaces. Topological spaces. Neighborhood and some concepts of topology. First and second countable spaces. Continuous functions. Limit, interior and boundary points. The notion of convergence. Separation axioms. T_0 , T_1 and Hausdorff spaces. Normal spaces. Urysohn’s and Tietze’s theorems. Product and quotient spaces. Compact spaces. Topological group. Theorems of metrization.