CRN 11982: HW 5

Problem 21. Exercise 3.2.2 (a-c)

Problem 22. Given a set $X$ of real numbers, let $L$ be the set of all limit points of $X$. Show that $L$ is closed.

Problem 23. Show: If $X$ is both open and closed, then $X={\mathbb R}$ or $X=\emptyset$.

Problem 24. Exercise 3.2.9 (a)

Problem 25. Find all limit points of the set

$$\left\{\frac{1}{m}+\frac{1}{n}\ :\ m,n\in\mathbb{N}\right\}$$ Remember that $A=B\ \Leftrightarrow\ (A\subseteq B)\wedge (B\subseteq A)$.