Two classical results characterizing regularity of a convergence space in
terms of continuous extensions of maps on one hand, and in terms of continuity
of limits for the continuous convergence on the other, are extended to
convergence-approach spaces. Characterizations are obtained for two alternative
extensions of regularity to convergence-approach spaces: regularity and strong
regularity. The results improve upon what is known even in the convergence
case. On the way, a new notion of strictness for convergence-approach spaces is
introduced.Comment: previous version had an error, fixed here with a new definition of
strictnes
