The single, most important concept in topology and analysis: Compactness. This is explained via covers, which I'll define as well. There are tons of applications of this concept, which you can find in the playlist below
Topology Playlist: https://youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGGBXRMV32EKVI
Other Compactness Video: https://youtu.be/xiWizwjpt8o
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