Obviously (C, [less than or equal to]) is a partially ordered set (
POSET).
Figure 1(middle) depicts the
poset [P.sub.[alpha]] the labels of the elements of [P.sub.[alpha]] refer to the corresponding faces of [G.sub.oct].
For a
poset X we denote its dual
poset by [X.sup.d].
We show that the operators of Section 3 provide a bijection f between a subfamily of WDI digraphs and finite
posets. When DI digraphs are considered, the range of f are precisely the dedekind complete finite
posets, i.e., the finite
posets that satisfy the least upper bound property.
Then ([A.sup.L], [less than or equal to]) is a
poset and the properties ([pBB.sup.L]), ([pM.sup.L]), (pEq[less than or equal to]) hold.
The following definitions give various induced relations by the order of a
poset.
Furthermore, the events in any set [[OMEGA].sub.[zeta]] are arranged according to the local causal relation [[right arrow].sub.[zeta]], which form the
poset ([[OMEGA].sup.[zeta]], [[OMEGA].sub.[zeta]]).
Let us observe that if X is an involution
poset, by it follows that c is bijective, and by (I1) and (I2) it holds that if x, y [member of] X are such that x < y, then [y.sup.c] < [x.sup.c].
Expansion of throughput capacity at
Poset to 9mtpy and construction of a new terminal at Vanino port (25mtpy throughput) should limit the bottlenecks normally seen at other Russian ports, especially in winter.
Then ( L, [less than or equal to]) is a
poset and for any x, y [member of] L, x [conjunction] y is the inf{x, y} and x [disjunction] y the sup{x, y}.
[6] Venkateswara Rao.J and Srinivasa Rao.K., "Pre [A.sup.*]-algebra as a
Poset", African Journal of Mathematics and Computer Science Research Vol.2 pp 073-080, May 2009.