An invitation to localic real functions

In the pointfree topological context of locales and frames, real functions on a locale L are represented as localic morphisms S(L)→ L(R) (i.e. frame homomorphisms L(R) → S(L)) where S(L) stands for the frame of all sublocales of L and L(R) denotes the frame of reals. This is reminiscent of dealing with (not necessarily continuous) real functions X → R as with continuous functions D(X)→ R where D(X) is the discrete space on the underlying set of X. But it is deeper: the structure of S(L) is rich enough to provide a nice common framework for the three types of continuity (lower semicontinuity, upper semicontinuity and continuity) as well as general (not necessarily continuous) real functions. The aim of this expository note is to provide a short overview of the theory of pointfree real functions and the strength of its applications.