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Semantic domains based on sets with families of equivalances. (English) Zbl 0917.68132

Jacobs, Bart (ed.) et al., Coalgebraic methods in computer science, CMCS ’98. Proceedings of the 1st workshop, Lisbon, Portugal, March 28–29, 1998. Amsterdam: Elsevier, Electronic Notes in Theoretical Computer Science. 11, electronic paper No. 6 (1998).
Summary: This paper contains a preliminary study of a class of spaces that can be seen as special cases of metric spaces. These spaces seem to cover all practical needs. Their interest lies mainly in the fact that the degree of mathematical sofistication required to develop the theory is quite small, at least as compared to the metric case. The paper recreates part of the theory developed for metric spaces, ending with a fixed-point theorem that can be used for solving “domain equations”, and a final coalgebra theorem.
For the entire collection see [Zbl 0903.00067].

MSC:

68Q55 Semantics in the theory of computing
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