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Partial dcpo's and some applications
We introduce partial dcpo's and show their some applications. A partial dcpo is a poset associated with a designated collection of directed subsets. We prove that (i) the dcpo-completion of every partial dcpo exists; (ii) for certain spaces X, the corresponding partial dcpo's of continuous real valued functions on X are continuous partial dcpos; (iii) if a space X is Hausdorff compact, the lattice of all S-lower semicontinuous functions on X is the dcpo-completion of that of continuous realdoi:10.5817/am2012-4-243 fatcat:7zchjyriovgnxkwt37lqsrbneq