Search results
Results from the WOW.Com Content Network
In mathematics and more specifically in topology, a homeomorphism (from Greek roots meaning "similar shape", named by Henri Poincaré), [2] [3] also called topological isomorphism, or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function.
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 ...
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 ...
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
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication.
The connecting homomorphism from H 0 (O V), which is simply the group O V (F) of F-valued points, to H 1 (μ 2) is essentially the spinor norm, because H 1 (μ 2) is isomorphic to the multiplicative group of the field modulo squares. There is also the connecting homomorphism from H 1 of the orthogonal group, to the H 2 of the kernel of the spin ...
For topological vector spaces: isomorphism of vector spaces which is also a homeomorphism of the underlying topological spaces. For Banach spaces: bijective linear isometry. For Hilbert spaces: unitary transformation. For Lie groups: a bijective smooth group homomorphism whose inverse is also a smooth group homomorphism.
A homeomorphism is an isomorphism of topological spaces. A diffeomorphism is an isomorphism of spaces equipped with a differential structure, typically differentiable manifolds. A symplectomorphism is an isomorphism of symplectic manifolds. A permutation is an automorphism of a set.