MAT 355 - 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.