MAT 355E - Intro. Topology

Course Objectives

1. To make the generalizations of some topics from analysis,
2. To teach connection between topological spaces and metric spaces,
3. To teach fundamental topics in topological spaces.

Course Description

Metric spaces. Topological spaces. Neighborhood and some concepts of topology. Limit, interior and
boundary points. The notion of convergence. Continuous functions . Product and quotient spaces.
Lindelof, first and second countable spaces. Seperable spaces. Separation axioms. T_0 , T_1 and
Hausdorff spaces. Regular and normal spaces. Urysohn’s and Tietze’s theorems. Compact spaces.
Connected spaces. Topological groups. Theorems of metrization.