4: Topology of the Real Line
( \newcommand{\kernel}{\mathrm{null}\,}\)
Thumbnail: The blue circle represents the set of points (x, y) satisfying x2+y2=r2. The red disk represents the set of points (x, y) satisfying x2+y2<r2. The red set is an open set, the blue set is its boundary set, and the union of the red and blue sets is a closed set. (Public Domain; Richard Giuly via Wikipedia)