• Announcements: Hello! Homework set HW2 is available online, as well as answers to HW1. As always, if you have questions, please send me an email or look for me on Zoom during office hours and I will be happy to discuss the details with you.

• Video 1: Definition of open cover and compact set
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• Video 2: Compactness is intrinsic: it does not depend on ''ambient'' space
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• Video 3: Compact subsets are closed
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• Video 4: Closed subsets of compact sets are compact
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• Video 5: Intersections of certain families of compact sets are nonempty
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• Video 6: Intersections of sequences of nested (nonempty) compact sets are nonempty
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• Video 7: Intersections of sequences of nested (nonempty) closed intervals are nonempty
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• Video 8: Infinite subsets of compact sets have a limit point
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• Video 9: Definition of $k$-cell, intersections of sequences of nested $k$-cells are nonempty
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• Video 10: $k$-cells are compact (in particular, closed intervals are compact)
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The final main result in this section of baby Rudin, the Heine-Borel Theorem, will be proven in the beginning of the next lecture.

• Lecture Notes (static file from above videos): PDF file