In order theory, a branch of mathematics, an order embedding is a special kind of monotone function, which provides a way to include one partially ordered set into another. Like Galois connections, order embeddings constitute a notion which is strictly weaker than the concept of an order isomorphism. Both of these weakenings may be understood in terms of category theory.
In order theory, a branch of mathematics, an orderembedding is a special kind of monotone function, which provides a way to include one partially ordered...
derivative is everywhere injective. An embedding, or a smooth embedding, is defined to be an immersion that is an embedding in the topological sense mentioned...
That is, it is a bijective order-embedding. It is also possible to define an order isomorphism to be a surjective order-embedding. The two assumptions that...
a surjective order-embedding. Hence, the image f(P) of an order-embedding is always isomorphic to P, which justifies the term "embedding". A more elaborate...
{\displaystyle \leq .} If an order-embedding between two posets S and T exists, one says that S can be embedded into T. If an order-embedding f : S → T {\displaystyle...
embedded, embed, or embedding in Wiktionary, the free dictionary. Embedded or embedding (alternatively imbedded or imbedding) may refer to: Embedding...
In natural language processing (NLP), a word embedding is a representation of a word. The embedding is used in text analysis. Typically, the representation...
In linguistics, center embedding is the process of embedding a phrase in the middle of another phrase of the same type. This often leads to difficulty...
An embedded system is a computer system—a combination of a computer processor, computer memory, and input/output peripheral devices—that has a dedicated...
distribute over arbitrary meets. Completion. A completion of a poset is an order-embedding of the poset in a complete lattice. Completion by cuts. Synonym of...
In mathematics, the Segre embedding is used in projective geometry to consider the cartesian product (of sets) of two projective spaces as a projective...
ordered set, a completion of S means a complete lattice L with an order-embedding of S into L. The notion of complete lattice generalizes the least-upper-bound...
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings in a book, a collection of half-planes all having the...
location of atom i {\displaystyle i} , and F {\displaystyle F} is an embedding function that represents the energy required to place atom i {\displaystyle...
that an orderembedding between partially ordered sets is injective. Clearly, every isometry between metric spaces is a topological embedding. A global...
"isolates". An "embedding" signals that a piece of text is to be treated as directionally distinct. The text within the scope of the embedding formatting characters...
Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded into...
are orderembeddings (functions for which x ≤ y {\displaystyle x\leq y} if and only if f ( x ) ≤ f ( y ) ) {\displaystyle f(x)\leq f(y))} and order isomorphisms...
W^{\ell ,q}(\mathbf {R} ^{n})} and the embedding is continuous. In the special case of k = 1 and ℓ = 0, Sobolev embedding gives W 1 , p ( R n ) ⊆ L p ∗ ( R...
algebra Monotonic Pointwise order of functions Galois connection Order embeddingOrder isomorphism Closure operator Functions that preserve suprema/infima...
optimizes to find an embedding that aligns the tangent spaces. Maximum Variance Unfolding, Isomap and Locally Linear Embedding share a common intuition...
dimension d {\displaystyle d} , called embedding dimension. In the general case, we can have different embedding dimensions for the entities d {\displaystyle...
planar graph. A 1-outerplanar embedding of a graph is the same as an outerplanar embedding. For k > 1 a planar embedding is k-outerplanar if removing the...
can flatten an appreciable amount in the order of thousandths of an inch. In critical fastener joints, embedment can mean loss of preload. Flattening of...
footprint and is well-suited for embedding in applications which require high-performance and concurrency. As with most embedded database systems, HailDB is...
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