Open Covers and Compact Sets - 8

If we were to summarize what we’ve learned so far in this course about infinite sets, we might say: infinite sets are cool, but they can have some weird and unexpected features. By contrast, we know much more about what to expect from finite sets: they’re closed, they’re bounded above and below, they always have maxima and minima, and any process (like a program) on a finite set terminates. In the next three lectures, we’ll study compact sets. We could think of these sets as sets that are “the next best thing” to being finite in that they share the nice features described above.

Reading: Rudin Chapter 2: Compact sets (page 36)

Pre-Lecture Materials

• Open covers and compact sets: Pre-lecture reading
• Open covers and compact sets: Full lecture notes

Open covers and compactness: Pre-lecture video A

Perfect sets: Pre-lecture video B

In-Class Activities

Open the following Overleaf link and make a copy for yourself. Remember to include the names of everyone who worked together in the document.

Lecture 8 In-Class Activity: Open Covers and Compact Sets

Assignments

• Submit Overleaf Proof 08: Compactness

Lecture Notes

• Lecture 8 Open Covers and Compact Sets CLASSNOTES S2026