  A classical result in Lorentzian geometry states that a strongly causal
spacetime is globally hyperbolic if and only if the Lorentzian distance is
finite valued for every metric choice in the conformal class. It is proven here
that a non-total imprisoning spacetime is globally hyperbolic if and only if
for every metric choice in the conformal class the Lorentzian distance is
continuous. Moreover, it is proven that a non-total imprisoning spacetime is
causally simple if and only if for every metric choice in the conformal class
the Lorentzian distance is continuous wherever it vanishes. Finally, a strongly
causal spacetime is causally continuous if and only if there is at least one
metric in the conformal class such that the Lorentzian distance is continuous
wherever it vanishes.
