Theoretical Computer Science
A Duality Theory for Quantitative Semantics
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Theoretical Computer Science - Mathematical foundations of programming semantics
Compactly generated domain theory
Mathematical Structures in Computer Science
On the Relationship between Filter Spaces and Weak Limit Spaces
Electronic Notes in Theoretical Computer Science (ENTCS)
Elementary Differential Calculus on Discrete and Hybrid Structures
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Electronic Notes in Theoretical Computer Science (ENTCS)
Injective Convergence Spaces and Equilogical Spaces via Pretopological Spaces
Electronic Notes in Theoretical Computer Science (ENTCS)
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The category TOP of topological spaces is not cartesian closed, but can be embedded into the cartesian closed category CONV of converyence spaces. It is well known that the category DCPO of dcpos and Scott continuous functions can be embedded into TOP, and so into CONV, by considering the Scott topology. We propose a different, "cotopological" embedding of DCPO into CONV, which, in contrast to the topological embedding, preserves products. If X is a cotopological dcpo, i.e. a dcpo with the cotopological CONV-structure, and Y is a topological space, then [X → Y] is again topological, and conversely, if X is a topological space, and Y a cotopological complete lattice, then [X → Y] is again a cotopological complete lattice. For a dcpo D, the topological and the cotopological convergence structures coincide if and only if D is a continuous dcpo. Moreover, cotopological dcpos still enjoy some of the properties which characterise continuous dcpos. For instance, all cotopological complete lattices are injective spaces (in CONV) w.r.t. topological subspace embeddings.