In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.
Let P be a partially ordered set and let Pp denote the set of all order-preserving mappings of P to P ordered by/ b in a partially ordered set X, a covers b if a > c > b implies a = c. Let V(X) denote the set of elements of X with a unique lower cover in X. Let Xd denote the dual
A partially ordered set (X, is called sharply transitive if its automorphism group is sharply transitive on X, that is, it is transitive and the stabilizer of every element is triviaL It is shown that every free group is the automorphism group of a sharply transitive partially or
The relative rank rank(S : U) of a subsemigroup U of a semigroup S is the minimum size of a set V ⊆ S such that U together with V generates the whole of S. As a consequence of a result by Sierpiński it follows that for U ≤ TX , the monoid of all self-maps of an infinite set X, ra
The results' in this paper were motivated by a search for the answers to the following questions : When can a given partially ordered algebra be embedded in a complete partially ordered algebra in such a fashion that the original algebra is dense and that the operations acquire o
' Formal methods for the description of spatial relations can be based on mathematical theories of order. queries about inclusion and coxtainment of spatiai areas. afteia u.iijni-or.tion to the basic concepts ol posets and lattices, their applications to modeilin! rputrut relatio
We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant distributions. We study a number of special cases,