Effectiveness for Embedded Spheres and Balls

@article{Miller2002EffectivenessFE,
  title={Effectiveness for Embedded Spheres and Balls},
  author={Joseph S. Miller},
  journal={Electr. Notes Theor. Comput. Sci.},
  year={2002},
  volume={66},
  pages={127-138}
}
We consider arbitrary dimensional spheres and closed balls embedded in Rn as Π1 classes. Such a strong restriction on the topology of a Π1 class has computability theoretic repercussions. Algebraic topology plays a crucial role in our exploration of these consequences; the use of homology chains as computational objects allows us to take algorithmic advantage of the topological structure of our Π1 classes. We show that a sphere embedded as a Π1 class is necessarily located, i.e., the distance… CONTINUE READING
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