  We consider a smooth submanifold $N$ with a smooth boundary in an ambient
closed manifold $M$ and assign a spectral invariant $c(\alpha,H)$ to every
singular homological class $\alpha\in H_*(N)$ and a Hamiltonian $H$ defined on
the cotangent bundle $T^*M$. We also derive certain properties of spectral
numbers, for example we prove that spectral invariants $c_\pm(H,N)$ associated
to the whole Floer homology $HF_*(H,N:M)$ of the submanifold $N$, are limits of
the decreasing nested family of open sets.
