  In this paper we prove that every pure-state $\Psi ^{(N)}$ of N (N$\geqslant
3)$ continuous variables corresponds to a pair of convex rigid covers (CRCs)
structures in the continuous-dimensional Hilbert-Schmidt space. Next we
strictly define what are the partial separability and ordinary separability,
and discuss how to use CRCs to describe various separability. We discuss the
problem of the classification of $\Psi ^{(N)}$ and give a kinematical
explanation of the local unitary operations acting upon $\Psi ^{(N)}$. Thirdly,
we discuss the invariants of classes and give a possible physical explanation.
