Halfordered sets, halfordered chain structures and splittings by chains

Abstract

Let (P, G 1 , G 2 ) be a 2-net where the set C of chains is not empty and let K s be a splitting of P by a chain K ∈ C. Then there correspond two halforders ξ l , ξ r of the set K which are related, and vice versa, if there are given two related halforders of K then there exists a splitting of P by K. The questions "when is ξ l = ξ r ?", "when is ξ l convex or an order?" will be studied. Moreover it will be shown that (P, G 1 , G 2 , {K s }) can be embedded in a halfordered chain structure in the sense of [1]. (2000): 53A60. Mathematics Subject Classification

Properties of Auto- and Antiautomorphisms of Maximal Chain Structures and their Relations to i-Perspectivities

“…Kroll in [5] and used by further authors (B. Alinovi, E. Gabrieli, B. Im, J. Kosiorek, A. Matraś and C. Tonesi c.f. [1][2][3][4] and [7]). In these papers we find a begin of a theory of chain structures.…”