Computable Operations on Compact Subsets of Metric Spaces with Applications to Fréchet Distance and Shape Optimization
  We extend the Theory of Computation on real numbers, continuous real
functions, and bounded closed Euclidean subsets, to compact metric spaces
$(X,d)$: thereby generically including computational and optimization problems
over higher types, such as the compact 'hyper' spaces of (i) nonempty closed
subsets of $X$ w.r.t. Hausdorff metric, and of (ii) equicontinuous functions on
$X$. The thus obtained Cartesian closure is shown to exhibit the same
structural properties as in the Euclidean case, particularly regarding function
pre/image. This allows us to assert the computability of (iii) Fréchet
Distances between curves and between loops, as well as of (iv)
constrained/Shape Optimization.
