  New theories of electroweak symmetry breaking have recently been constructed
that stabilize the weak scale and do not rely upon supersymmetry. In these
theories the Higgs boson is a weakly coupled pseudo-Goldstone boson. In this
note we study the class of theories that can be described by theory spaces and
show that the fundamental group of theory space describes all the relevant
classical physics in the low energy theory. The relationship between the low
energy physics and the topological properties of theory space allow a
systematic method for constructing theory spaces that give any desired low
energy particle content and potential. This provides us with tools for
analyzing and constructing new theories of electroweak symmetry breaking.
