  A type-2 computable real function is necessarily continuous; and this remains
true for relative, i.e. oracle-based computations. Conversely, by the
Weierstrass Approximation Theorem, every continuous f:[0,1]->R is computable
relative to some oracle.
  In their search for a similar topological characterization of relatively
computable multivalued functions f:[0,1]=>R (aka relations), Brattka and
Hertling (1994) have considered two notions: weak continuity (which is weaker
than relative computability) and strong continuity (which is stronger than
relative computability). Observing that uniform continuity plays a crucial role
in the Weierstrass Theorem, we propose and compare several notions of uniform
continuity for relations. Here, due to the additional quantification over
values y in f(x), new ways of (linearly) ordering quantifiers arise, yet none
of them turn out as satisfactory.
  We are thus led to a notion of uniform continuity based on the Henkin
Quantifier; and prove it necessary for relative computability. In fact
iterating this condition yields a strict hierarchy of notions each necessary,
and the omega-th level also sufficient, for relative computability.
