The Universal covering as a Hausdorff Topological Space

An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves by Dr. T.E. Venkata Balaji, Department of Mathematics, IIT Madras. For more details on NPTEL visit http://www.nptel.iitm.ac.in/syllabus/...

Goals of Lecture 13:

To ask the question as to why the fundamental group of a space occurs as a subgroup of automorphisms of its universal covering

To define the universal covering space intuitively as a space of paths

To give a natural topology on the space defined above and to show that this topology is Hausdorff

Keywords for Lecture 13:

Path, Fixed-end-point (FEP) homotopy equivalence class, fundamental group, pathwise or arcwise connected, Hausdorff, locally simply connected, universal covering, basic open set, base for a topology, sub-base for a topology