Examples of 'poset' in a sentence
Meaning of "poset"
Poset is a mathematical concept in order theory, a set equipped with a partial order relation. It is used as a noun in mathematics to refer to a partially ordered set, where any two elements are comparable
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- A partially ordered set.
How to use "poset" in a sentence
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poset
Forcing with this poset collapses λ down to κ.
An algebraic lattice is a complete lattice that is algebraic as a poset.
A chain is a subset of a poset that is linearly ordered.
Every poset that is a complete semilattice is also a complete lattice.
See also poset topology.
A poset in which every two elements are incomparable is called an antichain.
The coproduct of a poset category is the join operation.
Ideals are proper if they are not equal to the whole poset.
Not every poset has a deviation.
The most basic example is given by the least element of a poset.
Every finite poset is directed complete.
Locally finite poset.
Such a poset is called algebraic.
It is not known whether similar algebras exist for every differential poset.
Now we have a poset of worlds.
See also
A set with a partial order is called a partially ordered set also called a poset.
P is a poset with order.
At this work several aspects of codes embedded in spaces with poset metrics are studied.
Considering spaces embedded with poset metrics several metric aspects of codes has been studied.
A poset antimatroid has as its feasible sets the lower sets of a finite partially ordered set.
A chain antimatroid is the special case of a poset antimatroid for a total order.
The Hasse graph is a visualization of the ordering of the root poset.
A strict Sperner poset is a graded poset in which all maximum antichains are rank levels.
Also, every preordered set is equivalent to a poset.
The poset P is a continuous poset if it has some base.
Trivially every finite poset satisfies both ACC and DCC.
Every poset C can be completed in a completely distributive lattice.
Axiom 2 is equivalent to saying that the poset is a graded poset.
Debbie Mehlman and Sharon Poset were also raised by families of different faiths.
In particular the two-element discrete poset is not a lattice.
A poset D is a dcpo if and only if each chain in D has a supremum.
Given a locally finite poset P we can define its incidence algebra.
A poset is a sup-lattice if there is a supremum for every subset.
Indeed, the word length makes this into a graded poset.
A poset P in which any two.
The relation → is a partial order on those equivalence classes ; it defines a poset.
The map from the poset P to the complete Boolean algebra B is not injective in general.
More formally, a commutative diagram is a visualization of a diagram indexed by a poset category.
For example, a poset is locally finite if every closed interval in it is finite.
In mathematical order theory, an ideal is a special subset of a partially ordered set poset.
A subset of a poset is downward-directed if and only if its upper closure is a filter.
We have also introduced the notion of a cooperative game on a set-coloured poset.
Every such poset has a dual poset, formed by reversing all of the order relations.
Hence it is important to distinguish between a bounded-complete poset and a bounded complete partial order cpo.
To prove that it follows from the original form, let A be a poset.
For example, the poset of subobjects of any given object A is a bounded lattice.
An ideal I is prime if its set-theoretic complement in the poset is a filter.
Then the poset of cells of L, ordered by the inclusion of their closures, is Eulerian.
The concept of Euler characteristic of a bounded finite poset is another generalization, important in combinatorics.
A poset ( short for partially ordered set ) is a set with a partial order.
