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A story within a story, also referred to as an embedded narrative, is a literary device in which a character within a story becomes the narrator of a second story (within the first one). [1] Multiple layers of stories within stories are sometimes called nested stories .
Ideally the class of all embedded subobjects of a given object, up to isomorphism, should also be small, and thus an ordered set. In this case, the category is said to be well powered with respect to the class of embeddings. This allows defining new local structures in the category (such as a closure operator).
An embedded submanifold (also called a regular submanifold), is an immersed submanifold for which the inclusion map is a topological embedding. That is, the submanifold topology on S {\displaystyle S} is the same as the subspace topology.
One can tell if a sentence is center embedded or edge embedded depending on where the brackets are located in the sentence. [Joe believes [Mary thinks [John is handsome.]]] The cat [that the dog [that the man hit] chased] meowed. In sentence (1), all of the brackets are located on the right, so this sentence is right-embedded.
In natural language processing, a word embedding is a representation of a word. The embedding is used in text analysis.Typically, the representation is a real-valued vector that encodes the meaning of the word in such a way that the words that are closer in the vector space are expected to be similar in meaning. [1]
For infinite dimensional manifolds, this is sometimes taken to be the definition of an immersion. [4] An injectively immersed submanifold that is not an embedding. If M is compact, an injective immersion is an embedding, but if M is not compact then injective immersions need not be embeddings; compare to continuous bijections versus homeomorphisms.
An embedded graph uniquely defines cyclic orders of edges incident to the same vertex. The set of all these cyclic orders is called a rotation system.Embeddings with the same rotation system are considered to be equivalent and the corresponding equivalence class of embeddings is called combinatorial embedding (as opposed to the term topological embedding, which refers to the previous ...
If Y is a Banach space, an equivalent definition is that the embedding operator (the identity) i : X → Y is a compact operator. When applied to functional analysis, this version of compact embedding is usually used with Banach spaces of functions. Several of the Sobolev embedding theorems are compact embedding theorems.