The category TOP of topological spaces is not cartesian closed, but can be embedded into the cartesian closed category CONV of convergence 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.
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