# 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} }

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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