Search results
Results From The WOW.Com Content Network
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 .
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 ...
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 ...
The embedding of X into Y is a compact operator: any bounded set in X is totally bounded in Y, i.e. every sequence in such a bounded set has a subsequence that is Cauchy in the norm ||•|| Y. If Y is a Banach space, an equivalent definition is that the embedding operator (the identity) i : X → Y is a compact operator.
In mathematics, one normed vector space is said to be continuously embedded in another normed vector space if the inclusion function between them is continuous. In some sense, the two norms are "almost equivalent", even though they are not both defined on the same space. Several of the Sobolev embedding theorems are continuous embedding theorems.
A latent space, also known as a latent feature space or embedding space, is an embedding of a set of items within a manifold in which items resembling each other are positioned closer to one another. Position within the latent space can be viewed as being defined by a set of latent variables that emerge from the resemblances from the objects.
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]
A planar graph is a graph that has such an embedding onto the Euclidean plane, and a toroidal graph is a graph that has such an embedding onto a torus. The genus of a graph is the minimum possible genus of a two-dimensional manifold onto which it can be embedded. empty graph 1. An edgeless graph on a nonempty set of vertices. 2.