• Corpus ID: 4521897

Computable Operations on Compact Subsets of Metric Spaces with Applications to Fréchet Distance and Shape Optimization

@article{Park2017ComputableOO,
  title={Computable Operations on Compact Subsets of Metric Spaces with Applications to Fr{\'e}chet Distance and Shape Optimization},
  author={Chan-Bong Park and Ji-won Park and Sewon Park and Dongseong Seon and Martin Ziegler},
  journal={ArXiv},
  year={2017},
  volume={abs/1701.08402}
}

• Chan-Bong Park, Ji-won Park, +2 authors M. Ziegler
• Published 29 January 2017
• Mathematics
• ArXiv

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) Frechet Distances between curves and between loops, as well as of (iv) constrained/Shape Optimization.