Topology Lecture 08: Basis for a Topology

After defining a basis for a topology, we present several propositions that illustrate how working with bases can simplify our life. We show that open sets and continuity can both be characterized in terms of basis elements. Finally, we give criteria for a collection of subsets to generate a topology on an arbitrary set.

00:00 Introduction
00:19 Definition: Basis for a Topology
01:19 Basis for metric spaces
04:02 Basis for discrete space
05:50 Prop: Basis Criterion
14:53 Prop: Continuity in terms of basis
20:20 Prop: When is a collection a basis for some topology?

This lecture follows Lee's "Introduction to topological manifolds", chapter 2.

A playlist with all the videos in this series can be found here:
   • Topology