How Compactness Was Invented

Want to restore the planet’s ecosystems and see your impact in monthly videos? The first 100 people to join Planet Wild with my code ABIDE4 will get the first month for free on me: https://planetwild.com/r/abidebyreaso... If you want to get to know them better first, check out their Yellowstone to Yukon mission: https://planetwild.com/r/abidebyreaso... The free PDF I made for you:   / abidebyreason   _____ This video is about Compactness, one of the most important concepts in higher mathematics. Sorry for the following typo. Let me know if you notice any others. I do my best to prevent this, but I almost always miss something. Correction: 09:29 Inner Product and Normed Vector Space should be switched _____ Related Videos: Topological Spaces video:    • The Hierarchy of Math Spaces   Banach Spaces video:    • Weird spaces where π = 4   Hilbert Spaces video:    • What is a Hilbert Space?   _____ Sources: A pedagogical history of compactness by Manya Raman-Sundström Compactness AND Compactification by Terence Tao Topology by James R. Munkres Helpful Stack Exchange Post: https://math.stackexchange.com/questi... Great video by Morphocular:    • The Concept So Much of Modern Math is Buil...   _____ Music: Epidemic Sound Animations created using Manim: https://www.manim.community/ Research, writing, voiceover, editing, animation: Dan Kosakowski Illustrations and thumbnails: Christine Kosakowski This video was sponsored by Planet Wild