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In graph theory, two graphs and ′ are homeomorphic if there is a graph isomorphism from some subdivision of to some subdivision of ′.If the edges of a graph are thought of as lines drawn from one vertex to another (as they are usually depicted in diagrams), then two graphs are homeomorphic to each other in the graph-theoretic sense precisely if their diagrams are homeomorphic in the ...
A chart of a manifold is a homeomorphism between an open subset of the manifold and an open subset of a Euclidean space. The stereographic projection is a homeomorphism between the unit sphere in R 3 {\displaystyle \mathbb {R} ^{3}} with a single point removed and the set of all points in R 2 {\displaystyle \mathbb {R} ^{2}} (a ...
A homomorphism from the flower snark J 5 into the cycle graph C 5. It is also a retraction onto the subgraph on the central five vertices. Thus J 5 is in fact homomorphically equivalent to the core C 5. In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure
Let M be a topological space.A chart (U, φ) on M consists of an open subset U of M, and a homeomorphism φ from U to an open subset of some Euclidean space R n.Somewhat informally, one may refer to a chart φ : U → R n, meaning that the image of φ is an open subset of R n, and that φ is a homeomorphism onto its image; in the usage of some authors, this may instead mean that φ : U → R n ...
The concept of homomorphism has been generalized, under the name of morphism, to many other structures that either do not have an underlying set, or are not algebraic. This generalization is the starting point of category theory. A homomorphism may also be an isomorphism, an endomorphism, an automorphism, etc. (see below). Each of those can be ...
But a local homeomorphism is a homeomorphism if and only if it is bijective. A local homeomorphism need not be a homeomorphism. A local homeomorphism need not be a homeomorphism. For example, the function R → S 1 {\displaystyle \mathbb {R} \to S^{1}} defined by t ↦ e i t {\displaystyle t\mapsto e^{it}} (so that geometrically, this map wraps ...
For a set of traits, the equation that describe the variance among traits is the multivariate breeder’s equation Δz = β x G, where Δz is the vector of differences in trait means, β is a vector of selection coefficients, and G is a matrix of the additive genetic variance and covariance between traits.
Multiple traits are used in this approach to examine (a) similar or (b) dissimilar traits , in order to establish convergent and discriminant validity between traits. Similarly, multiple methods are used in this approach to examine the differential effects (or lack thereof) caused by method specific variance.