MIT 18.100B Real Analysis, Spring 2025 - Lecture 13: Open and Closed Sets; Coverings; Compactness

MIT 18.100B Real Analysis, Spring 2025 Instructor: Tobias Holck Colding View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG We begin by giving a useful characterization of what it means for a set to be closed. This is the notion that a set contains all its limit points. After that, we turn to the notion of a cover and, in particular, open covers and use it to define compact subsets of a metric space. License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu Support OCW at http://ow.ly/a1If50zVRlQ We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.