MAT 605E - Topology

Course Objectives

1. To teach some of the high-level topics of Topology,
2. To form the necessary background for the graduate students who wish to do research on Topology.

Course Description

Topological Spaces and Continuous Functions: Basis for a Topology, The Product Topology, The Metric Topology, The Quotient Topology.
Connectedness and Compactness: Components and Path Components, Local Connectedness, Compact Spaces, Local Compactness.
Countability and Separation Axioms, The Urysohn Metrization Theorem, The Tychonoff Theorem Metrization Theorems and Paracompactness: The Smirnov Metrization Theorem.
Complete Metric Spaces and Function Spaces: The Compact-Open Topology, Ascoli’s Theorem, Baire Spaces.