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**1 - 9**of**9**### A Non-Topological View of Dcpo’s as Convergence Spaces. In

- Schellekens and A.K. Seda (Eds.), Proceedings of the First Irish Conference on the Mathematical Foundations of Computer Science and Information Technology
, 2003

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, 1998

"... We study continuous lattices with maps that preserve all suprema rather than only directed ones. We introduce the (full) subcategory of FS-lattices, which turns out to be -autonomous, and in fact maximal with this property. FS-lattices are studied in the presence of distributivity and algebraicity. ..."

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We study continuous lattices with maps that preserve all suprema rather than only directed ones. We introduce the (full) subcategory of FS-lattices, which turns out to be -autonomous, and in fact maximal with this property. FS-lattices are studied in the presence of distributivity and algebraicity. The theory is extremely rich with numerous connections to classical Domain Theory, complete distributivity, Topology and models of Linear Logic. 1.

### Linear Types and Approximation

, 1994

"... We enrich the -autonomous category of complete lattices and maps preserving all suprema with the important concept of approximation by specifying a -autonomous full subcategory LFS of linear FS-lattices . This is the greatest -autonomous full subcategory of linked bicontinuous lattices. The modalit ..."

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We enrich the -autonomous category of complete lattices and maps preserving all suprema with the important concept of approximation by specifying a -autonomous full subcategory LFS of linear FS-lattices . This is the greatest -autonomous full subcategory of linked bicontinuous lattices. The modalities !() and ?() mediate a duality between the upper and lower powerdomains. The distributive objects in LFS give rise to the compact closed -autonomous full subcategory CD of completely distributive lattices . We characterize algebraic objects in LFS by forbidden substructures "a la Plotkin'. Keywords: -autonomous category, linear logic, interaction orders, bicontinuous lattices, completely distributive lattices, upper and lower powerdomains. 1 Introduction Complete lattices with maps preserving all suprema as morphisms form a -autonomous category SUP [Bar79] and give rise to a model of linear logic in the standard fashion of [See89]. If 2 := f0 ! 1g denotes the two-point lattice and A...

### CONTINUOUS AND DUALLY CONTINUOUS IDEMPOTENT

"... O. R. Nykyforchyn. Continuous and dually continuous idempotent L-semimodules, Mat. Stud. ..."

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O. R. Nykyforchyn. Continuous and dually continuous idempotent L-semimodules, Mat. Stud.