# Sharp Elements and Apartness in Domains

@inproceedings{Jong2021SharpEA,
title={Sharp Elements and Apartness in Domains},
author={Tom de Jong},
booktitle={Mathematical Foundations of Programming Semantics},
year={2021}
}
• T. D. Jong
• Published in
Mathematical Foundations of…
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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