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