Let C be a totally ordered
subset of [C.sub.[phi]].
A non-empty subset C of E is called a chain or totally ordered
if all the elements of C are comparable.
To state our third main result and its important corollary (our Theorem 4), we need to recall a definition of the notion of lexicographic shellability of a poset: A finite graded poset P with a maximum and a minimum element is called EL-shellable (lexicographically shellable), if there exists a map f = [f.sub.[GAMMA]]: C(P) [right arrow] [GAMMA] between the set of covering relations C(P) of P into a totally ordered
set [GAMMA] satisfying
Notice that if (X, [[less than or equal to].sub.X]) is a totally ordered
set, the condition given in Theorem 3.3 is obviously satisfied and we obtain uniqueness of the fixed point.
In contrast, if one represents a plan with a totally ordered
sequence of concrete actions (as with McDermott's UNPOP), then it is easy to calculate the resulting state and thus heuristically estimate the distance to a desired goal state.
According to China Steel's statistic compilation, Taiwanese fastener makers totally ordered
236,700 metric tons of various wire rods in the third quarter alone, accounting for 54% of the total ordered during the period and hitting a 3-year high.
This volume collects ten papers from the June 2007 second Brussels Conference on Generative Linguistics addressing alternatives to cartography, which in the field of generative grammar refers to the idea that sentence structure can be represented as a template of fixed positions, each which can be filled by a limited set of syntactico-semantic elements, that are seen as universal totally ordered
sets of functional projections, the specifiers of which serve as merger sites or as landing sites for XP-movement.
The Totem multiple-ring protocol provides reliable totally ordered
delivery of messages across multiple local-area networks interconnected by gateways.
It includes as substructures not only the ordinals, but any other totally ordered
structure that can reasonably be regarded as a number system.
The article by Louise Moser, Michael Melliar-Smith, and their team at the University of California, Santa Barbara, describes the Totem system, which provides a totally ordered
multicast service to application process groups.
Moreover, it is to the holiness of the faithful that the hierarchical structure of the church is totally ordered
. For this reason, the declaration Inter Insigniores recalls: "The only better gift, which can and must be desired, is love (cf.
If the alphabet A is totally ordered
, and u, v [member of] [A.sup.*] are such that all letters in v are greater than the letters in u, we write alph(u) < alph(v).