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An embedding, or a smooth embedding, is defined to be an immersion that is an embedding in the topological sense mentioned above (i.e. homeomorphism onto its image). [ 4 ] In other words, the domain of an embedding is diffeomorphic to its image, and in particular the image of an embedding must be a submanifold .
In contrast, a closed text leads the reader to one intended interpretation. The concept of the open text comes from Umberto Eco 's collection of essays The Role of the Reader , [ 1 ] but it is also derivative of Roland Barthes 's distinction between 'readerly' ( lisible ) and 'writerly' (scriptible) texts as set out in his 1968 essay, " The ...
A smooth embedding is an injective immersion f : M → N that is also a topological embedding, so that M is diffeomorphic to its image in N. An immersion is precisely a local embedding – that is, for any point x ∈ M there is a neighbourhood, U ⊆ M, of x such that f : U → N is an embedding, and conversely a local embedding is an ...
In particular, a closed immersion is universally closed. A closed immersion is stable under base change and composition. The notion of a closed immersion is local in the sense that f is a closed immersion if and only if for some (equivalently every) open covering X = ⋃ U j {\displaystyle X=\bigcup U_{j}} the induced map f : f − 1 ( U j ...
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 ...
For example, if X and Y are smooth over a scheme S and if i is an S-morphism, then i is a regular embedding. In particular, every section of a smooth morphism is a regular embedding. [1] If is regularly embedded into a regular scheme, then B is a complete intersection ring. [2]
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]
A map is a local diffeomorphism if and only if it is a smooth immersion (smooth local embedding) and an open map. The inverse function theorem implies that a smooth map f : X → Y {\displaystyle f:X\to Y} is a local diffeomorphism if and only if the derivative D f x : T x X → T f ( x ) Y {\displaystyle Df_{x}:T_{x}X\to T_{f(x)}Y} is a linear ...