Closure functions on the set of positive integers. (English) Zbl 0852.04005

Shum, Kar-Ping

Sci. China, Ser. A 39, No. 4, 337-346 (1996).

The following question, raised by P. C. Hammer in 1960, is answered: Let \(M\) be the set of all positive integers, \(h\) the closure function under multiplication defined on the power set of \(M\) and \(c\) the complementation function. Do \(h\) and \(c\) generate exactly 14 distinct functions by composition in any order? Different types of sets which yield 14 distinct sets in the set of positive integers have also been found.

Reviewer: K.-P.Shum (Hongkong)

MSC:

03E05

Other combinatorial set theory

Keywords:

\(K\)-sets; algebraic boundary; closure function; complementation function