MIT 18.100B Real Analysis, Spring 2025 - Lecture 12: Convergence in Metric Spaces; Operations on Sets

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 continue our discussion of metric spaces and see that even more concepts that we have studied on the real line have counterparts in metric spaces. Those include, in addition to, sequences, convergence and Cauchy sequence also a ball, a bounded set, as well as open and closed subsets. 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.