  We show that any pair of classical solutions of open string field theory can
be related by a formal gauge transformation defined by a gauge parameter $U$
without an inverse. We investigate how this observation can be used to
construct new solutions. We find that a choice of gauge parameter consistently
generates a new solution only if the BRST charge maps the image of $U$ into
itself. When this occurs, we argue that $U$ naturally defines a star algebra
projector which describes a surface of string connecting the boundary conformal
field theories of the classical solutions related by $U$. We also note that
singular gauge transformations give the solution space of open string field
theory the structure of a category, and we comment on the physical
interpretation of this observation.
