Self-similar Sets as Tarski's Fixed Points

Then (D, !=) is a CPO with the bottom S, since every directed set in D has a non-empty intersection. Note that a topological space is compact if and only if its partially ordered set of non-empty closed sets (D, E) is a CPO. Any subset of D, say X, has the inf Y\X, which is the closure of \JX. Besides, fljfl ••• fl an is a continuous n-ary function, i. e. continuous with respect to each argument at. We will call this kind of CPO a spatial CPO. On the other hand, D is a compact Hausdorff space with the finite topology [6], which is generated by bases of the form