directed set वाक्य
उदाहरण वाक्य
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- Every dcpo is an ?-cpo, since every ?-chain is a directed set, but the converse is not true.
- Starting with an arbitrary set, you want to use the existence of finite joins to turn it into a directed set, as you thought.
- The requirement that the metric take values in [ 0, " ) can even be relaxed to consider metrics with values in other directed sets.
- Is there some reasonable example of a directed set that is not a poset ?-talk ) 02 : 06, 4 November 2008 ( UTC)
- Indeed, in the theory of metric spaces, sequences play a role that is in many aspects analogous to the role of directed sets in domain theory.
- The compact elements of a domain have the important special property that they cannot be obtained as a limit of a directed set in which they did not already occur.
- This leads to the class of continuous posets, consisting of posets where every element can be obtained as the supremum of a directed set of elements that are algebraic.
- It was established by an Act of the Virginia House of Burgesses in 1691, when each county in the Virginia Colony was directed set aside of land for a town.
- Requiring the existence of directed suprema can be motivated by viewing directed sets as generalized approximation sequences and suprema as " limits " of the respective ( approximative ) computations.
- It seems to me that the collection of all finite cyclic groups also forms a direct system of groups over the directed set of natural numbers ordered ( dually ) by divisibility.
- For the case of a join-semilattice note that any set can be turned into a directed set with the same supremum by closing under finite ( non-empty ) suprema.
- Then just argue that the least upper bound of the resulting directed set is a least upper bound of the original set .-- talk ) 00 : 24, 30 May 2011 ( UTC)
- Naturally, one has a special interest in those domains of computations in which all consistent specifications " converge ", i . e . in orders in which all directed sets have a least upper bound.
- From the article on Power domains : " P " [ D ] is the collection of downward-closed subsets of domain D that are also closed under existing least upper bounds of directed sets in D.
- One says it is a "'directed family of seminorms "'if the family is a directed set with addition as the join, in other words if for every and, there is a such that.
- A topology is order consistent with respect to a certain order d " if it induces d " as its specialization order and it has the above property of inaccessibility with respect to ( existing ) suprema of directed sets in d ".
- This generalization exhibits the Riemann Stieltjes integral as the Moore Smith limit on the directed set of partitions of [ " a ", " b " ] . calls it the "'Pollard Moore Stieltjes integral " '.
- In general, however, it has an approximate identity which is a net ( or generalized sequence ) \ { e _ i \ } _ { i \ in I } indexed on a directed set I such that f * e _ i \ to f.
- In the mathematical area of order theory, the "'compact "'or "'finite elements "'of a partially ordered set are those elements that cannot be subsumed by a supremum of any non-empty directed set that does not already contain members above the compact element.
- According to what was said above, this would be an element that is the most general piece of information that extends the information of all elements of the directed set, i . e . the unique element that contains " exactly " the information that was present in the directed set-and nothing more.
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