  We study a regular closure operator in the category of quandles. We show that
the regular closure operator and the pullback closure operator corresponding to
the reflector from the category of quandles to its full subcategory of trivial
quandles coincide, we give a simple description of this closure operator, and
analyze some of its properties. The category of algebraically connected
quandles turns out to be a connectedness in the sense of Arhangel'ski\v{\i} and
Wiegandt corresponding to the full subcategory of trivial quandles, while the
disconnectedness associated with it is shown to contain all quasi-trivial
quandles. The separated objects for the pullback closure operator are precisely
the trivial quandles. A simple formula describing the effective closure
operator on congruences corresponding to the same reflector is also given.
