  A band gap for electronic states in crystals governs various properties of
solids, such as transport, optical and magnetic properties. Its estimation and
control have been an important issue in solid state physics. The band gap can
be controlled externally by various parameters, such as pressure, atomic
compositions and external field. Sometimes, the gap even collapses by tuning
some parameter. In the field of topological insulators, such closing of the gap
at a time-reversal invariant momentum indicates a band inversion, i.e. it leads
to a topological phase transition from a normal insulator to a topological
insulator. Here we show that the gap losing in inversion-asymmetric crystals is
universal, in the sense that the gap closing always leads either to a Weyl
semimetal or a nodal-line semimetal, from an exhaustive study on possible space
groups. We here consider three-dimensional spinful systems with time-reversal
symmetry. The space group of the system and the wavevector at the gap closing
uniquely determine which possibility occurs and where the gap-closing points or
lines lie in the wavevector space after closing of the gap. In particular, we
show that an insulator-to-insulator transition never happens, which is in sharp
contrast with inversion-symmetric systems.
