Self-similar Sets as Tarski's Fixed Points | Zendy

Susumu Hayashi | Zendy

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Self-similar Sets as Tarski's Fixed Points

Author(s) -

Susumu Hayashi

Publication year - 1985

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195178796

Subject(s) - mathematics , intersection (aeronautics) , closure (psychology) , hausdorff space , continuous function (set theory) , topological space , compact space , closed set , space (punctuation) , set (abstract data type) , function (biology) , discrete mathematics , argument (complex analysis) , pure mathematics , topology (electrical circuits) , combinatorics , computer science , evolutionary biology , economics , engineering , market economy , biology , programming language , aerospace engineering , biochemistry , chemistry , operating system

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

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