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Lecture 5: Complete Metric Spaces episode artwork

Oct 29, 2026 1 hr 17 min

Lecture 5: Complete Metric Spaces

from MIT OpenCourseWare: Free Courses from the institute Hosted by MIT OpenCourseWare

MIT 18.S190 Introduction To Metric Spaces, IAP 2023Instructor: Paige BrightUploaded 22-05-23View 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=PLUl4u3cNGP613ULTyHAqz04niYf722x7SNot every metric space is a complete metric space, but for those that are we can prove some important concepts. We prove the Banach Fixed Point theorem and prove that we can “complete” (or “fill in the holes” of) every metric space.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-SAMore information at https://ocw.mit.edu/termsMore courses at https://ocw.mit.eduSupport OCW at http://ow.ly/a1If50zVRlQWe 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.

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Lecture 5: Complete Metric Spaces

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