Convex subsets of partial monounary algebras

Abstract

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On directed convex subsets of partial monounary algebras

“…Remark. The author wishes to correct an inaccuracy in the definition of convexity in [2]; namely, the assumption "not containing the element 62 twice" (cf. Definition 0.1 above), was not expressed in [2].…”

“…The author wishes to correct an inaccuracy in the definition of convexity in [2]; namely, the assumption "not containing the element 62 twice" (cf. Definition 0.1 above), was not expressed in [2]. In the whole paper [2] the convexity is to be understood in the sense of the above Definition O.L For (A,f) G <?/ let DC(^,/) and DuC(A/) be as in the introduction.…”

“…Definition 0.1 above), was not expressed in [2]. In the whole paper [2] the convexity is to be understood in the sense of the above Definition O.L For (A,f) G <?/ let DC(^,/) and DuC(A/) be as in the introduction. Both the systems DC(^4, /) and DuC(,4, /) are considered to be partially ordered by inclusion; the empty set is the least element in both DC(v4,/) and X)\\C(A,f).…”

“…This paper can be considered to be a continuation of [2], [3] and [4]; in these papers analogous problems concerning the system of all convex subsets and the system of all intervals of a partial monounary algebra have been studied.…”

“…x = a,(3) x = /(a)^a,(4) x = /'(a) for some t 6 N, t > 1 and x g {/ I "" 1 (a)i/ I '"2 (a)}-If (1) is valid, then 4.LI (1) implies that x G domg and g(x) = f(x) = y, thus d g (x,y) = 1. Let (2) hold.…”