  Dirac points (DP) in Hermitian systems play a key role in topological
phenomena. Their existence in non-Hermitian systems is then desirable, but the
addition of loss or gain transforms DPs into pairs of Exceptional Points (EPs)
joined by a Fermi arc, which exhibit interesting but different properties. When
the transition to a non-Hermitian system results from the opening of a
radiation channel, the system can also support bound states in the continuum
(BICs), which are non-radiative resonant states that appear within the band of
radiation states. We theoretically show that simultaneous band-crossing of two
BICs can prevent the formation of EPs and Fermi arcs, resulting in genuine
Hermitian DPs, which are nonetheless embedded in the continuum of radiation
states. Dirac points embedded in the continuum (DECs) are a new topological
entity that combines the rich physics associated with DPs with the ideal
resonant properties of BICs in non-Hermitian systems.
