A non-topological view of dcpos as convergence spaces.
The familiar embedding of the category \textbf{DCPO} of dcpos and Scott--continuous functions by means of the Scott topology lacks some desirable properties: It does not preserve products, binary joins are not always continuous in the proper topological sense, and pointwise joins of continuous functions \(X\rightarrow L_c\) may fail to be continuous. The author constructs an embedding \(D\) from \textbf{DCPO} into the category \textbf{CONV} of convergence spaces that is free from the above deficiencies. Moreover he demonstrates that the convergence spaces appearing in the image of \(D\), which he calls \textit{cotopological dcpos}, enjoy many interesting properties familiar from continuous dcpos and behave rather well with respect to the formations of function spaces. For a dcpo \(D\), its topological structure agrees with its cotopological convergence structure if and only if \(D\) is a continuous dcpo.
scientific article; zbMATH DE number 2055972
scientific article