An Example of a Compactification of the Open Interval (0,1) With the Euclidean Topology
Let
be a topological space. A compactification of
is a topological space
such thatis homeomorphic to a dense subspace of
Note that a set
is dense in a set if
Possible compactifications of
are to the unit circle
with one point removed,
considered as a subspace of the unit circle and the closed interval
considered as a subspace of
is dense insince
and
is dense in
since
- note the pointsand
are defined to be the same point.
