  In these expository notes, intended for students without background in
point-set topology, we develop the basic theory of the Stone-Cech
compactification without reference to open sets, closed sets, filters, or nets.
In particular, this means we cannot use any of the usual definitions of
topological space. This may seem like proposing to run a marathon while hopping
on one foot, but it is easier than it may appear, and not devoid of interest.
We use gauge spaces (uniform spaces presented by a family of pseudometrics); we
define compactness as total boundedness plus completeness; and we define
completeness using a variation on Lawvere's categorical characterization of
completeness for metric spaces.
