Closure and Nested Intervals - 6 & Quiz 1

In today’s class, we’ll introduce the idea of set closure. We will also discuss whether infinite intersections of nested sets are empty or not. Next time, we’ll see what is required of the nested sets to ensure that their intersection is non-empty.

Reading: Rudin Chapter 2: Metric Spaces (pg. 32,35), with some additional material not in Rudin

Note

Today is Quiz 1 - in class.

Pre-Lecture Materials

Closure and nested intervals: Pre-lecture video A

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 6 In-Class Activity: Nested Intervals

Assignments

  • Submit Overleaf Proof 06: Nested Interval Theorem
  • Homework 3

Lecture Notes