Lecture 4: Compact Metric Spaces

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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 prove four concepts of compactness are equivalent in this lecture. We use the Lebesgue Number Lemma, Cantor’s Intersection Theorem, Cauchy completeness, and totally bounded sets to do so. 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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