MIT's 18.100B Real Analysis course, taught by Tobias Holck Colding, continues with a lecture on the topology of metric spaces. Colding opens with a characterization of closed sets as those containing all their limit points, building on the earlier definitions of open sets and limit points. He then introduces the idea of a cover, focusing on open covers, and uses that machinery to define compactness for subsets of a metric space. The eighty-minute session is blackboard-based, with Colding working through definitions and proofs step by step, the standard format for this OCW series. This is one lecture in a full-semester undergraduate analysis sequence, pitched at students who already have the basics of metric spaces and continuity under their belt.