I learned that the union of open sets is always open and the intersection of a finite set of open sets is open. However, the intersection of an infinite number of open sets can be closed. Apparently, the following example illustrates this.
In $E^2$, let $X$ be the infinite family of concentric open disks of radius $1 + 1/n$ for all $n \in \mathbb{Z^+}$. Why is $X$ a closed set? Can't I create a boundary set for $X$ that encloses all the elements in the interior?