  Continuous functions on the unit interval are relatively tame from the
logical and computational point of view. A similar behaviour is exhibited by
continuous functions on compact metric spaces equipped with a countable dense
subset. It is then a natural question what happens if we omit the latter 'extra
data', i.e. work with 'unrepresented' compact metric spaces. In this paper, we
study basic third-order statements about continuous functions on such
unrepresented compact metric spaces in Kohlenbach's higher-order Reverse
Mathematics. We establish that some (very specific) statements are classified
in the (second-order) Big Five of Reverse Mathematics, while most
variations/generalisations are not provable from the latter, and much stronger
systems. Thus, continuous functions on unrepresented metric spaces are 'wild',
though 'more tame' than (slightly) discontinuous functions on the reals.
