  We study the stability of gap-closing (Weyl or Dirac) points in the
three-dimensional Brillouin zone of semimetals using Clifford algebras and
their representation theory. We show that a pair of Weyl points with
$\mathbb{Z}_2$ topological charge are stable in a semimetal with time-reversal
and reflection symmetries when the square of the product of the two symmetry
transformations equals minus identity. We present toy models of $\mathbb{Z}_2$
Weyl semimetals which have surface modes forming helical Fermi arcs. We also
show that Dirac points with $\mathbb{Z}_2$ topological charge are stable in a
semimetal with time-reversal, inversion, and SU(2) spin rotation symmetries
when the square of the product of time-reversal and inversion equals plus
identity. Furthermore, we briefly discuss the topological stability of point
nodes in superconductors using Clifford algebras.
