Lecture 3: Compact Sets in Rⁿ

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MIT 18.S190 Introduction To Metric Spaces, IAP 2023 Instructor: Paige Bright View the complete course: https://ocw.mit.edu/courses/18-s190-introduction-to-metric-spaces-january-iap-2023/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP613ULTyHAqz04niYf722x7S We motivate the concept of compact sets on Euclidean space with norms, support of functions, and finite sets. We also prove the Heine-Borel theorem and introduce the notions of topological and sequential compactness. This video has been dubbed using an artificial voice via https://aloud.area120.google.com to increase accessibility. You can change the audio track language in the Settings menu. 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.

Published 2023-05-22 · Watch on YouTube ↗
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