An Example of a Compactification of the Open Interval (0,1) With the Euclidean Topology

Letbe a topological space. A compactification ofis a topological space such thatis homeomorphic to a dense subspace ofNote that a setis dense in a set if

Possible compactifications ofare to the unit circlewith one point removed,considered as a subspace of the unit circle and the closed intervalconsidered as a subspace of

is dense insinceandis dense insince- note the pointsandare defined to be the same point.