On the continuity of the feasible set in extremally linear problems

The purpose of this paper is to investigate continuity properties of the feasible set in extremally linear problems. Feasible sets of such problems are subsets of Fⁿ (the n-fold cartesian product of a fully ordered group (F,º)) and are described by a finite or an infinite number of inequalities or equalities, which are linear with respect to the operations ? and º. Thereby, the operation ? is induced by the fully-order in F by setting x?y = y iff x ≤ y for x, y in F. In particular, we derive conditions for the upper- and lower-semi-continuity of the feasible-set-mapping Z and investigate the structure of certain parameter sets. Especially, we show that the compactness of the feasible set, resp. the condition that the closure of the set of the strict feasible points is the feasible set, is sufficient for the upper-semi-continuity (u.s.c), resp. the lower-semi-continuity (l.s.c.) of Z, but - unlike to semi-infinite linear optimization - is not necessary for the u.s.c, resp. l.s.c. If we restrict Z on a certain subset of the parameter set, these conditions are also necessary. This paper is a continuation of the author's work in 6] and 7].