  The notion of a spherical space over an arbitrary base scheme is introduced
as a generalization of a spherical variety over an algebraically closed field.
It is studied how the sphericity condition behaves in families. In particular
it is shown that sphericity of subgroup schemes is an open and closed condition
over arbitrary base schemes generalizing a result by Knop and Roehrle. Moreover
spherical embeddings are classified over arbitrary fields generalizing and
simplifying results by Huruguen.
