Equilogical spaces form a cartesian closed complete category that contains all T0 spaces. We first present the cartesian closed complete subcategory of ordered equilogical spaces that still contains all T0 spaces, but excludes certain pathological equilogical spaces. Then, we further restrict to the cartesian closed complete subcategory of equilogical d-spaces that still contains all dcpo's and all T1 spaces. Its main advantage is that equilogical d-spaces with least element admit a least fixed point operator.
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