Let
be a compact Hausdorff space and
the Banach space of all realvalued continuous
functions on , with the sup norm. Types over
(in the sense of Krivine and Maurey) are
represented here by pairs
of bounded realvalued functions on
, where is lower semicontinuous and
is upper semicontinuous,
and
for every isolated point
of
. For each pair the corresponding type is
defined by the equation
for all
, where
is the sup norm on bounded functions. The
correspondence between types and pairs
is bijective.
