Sharp Elements and Apartness in Domains

  title={Sharp Elements and Apartness in Domains},
  author={Tom de Jong},
  • T. D. Jong
  • Published in MFPS 28 December 2021
  • Mathematics
Working constructively, we study continuous directed complete posets (dcpos) and the Scott topology. Our two primary novelties are a notion of intrinsic apartness and a notion of sharp elements. Being apart is a positive formulation of being unequal, similar to how inhabitedness is a positive formulation of nonemptiness. To exemplify sharpness, we note that a lower real is sharp if and only if it is located. Our first main result is that for a large class of continuous dcpos, the Bridges–V… 



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