  The empty set of course contains no computable point. On the other hand,
surprising results due to Zaslavskii, Tseitin, Kreisel, and Lacombe assert the
existence of NON-empty co-r.e. closed sets devoid of computable points: sets
which are `large' in the sense of positive Lebesgue measure. We observe that a
certain size is in fact necessary: every non-empty co-r.e. closed real set
without computable points has continuum cardinality.
  This leads us to investigate for various classes of computable real subsets
whether they necessarily contain a (not necessarily effectively findable)
computable point.
