  We present a property equivalent to the property of being semi-Kelley. Using
this equivalence we prove that being semi-Kelley is a hereditary property for
atriodic continua. We prove that semi-Kelley remainders are atriodic, moreover,
we prove that semi-Kelley continua are semi-Kelley remainders for chainable
continua, circularly chainable continua, and arc continua, and we give an
example of an atriodic Kelley continuum which is a semi-Kelley remainder and
not a Kelley remainder. We also prove that hereditarily semi-Kelley dendroids
are smooth.
