  We propose a new type of topological states of matter exhibiting
topologically nontrivial edge states (ESs) within gapless bulk states (GBSs)
protected by both spin rotational and reflection symmetries. A model presenting
such states is simply comprised of a one-dimensional reflection symmetric
superlattice in the presence of spin-orbit coupling containing odd number of
sublattices per unit cell. We show that the system has a rich phase diagram
including a topological metal (TM) phase where nontrivial ESs coexist with
nontrivial GBSs at Fermi level. Topologically distinct phases can be reached
through subband gap closing-reopening transition depending on the relative
strength of inter and intra unit cell spin-orbit couplings. Moreover,
topological class of the system is AI with an integer topological invariant
called $\mathbb{Z}$ index. The stability of TM states is also analyzed against
Zeeman magnetic fields and on-site potentials resulting in that the spin
rotational symmetry around the lattice direction is a key requirement for the
appearance of such states. Also, possible experimental realizations are
discussed.
