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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 ...
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 algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces).The word homomorphism comes from the Ancient Greek language: ὁμός (homos) meaning "same" and μορφή (morphe) meaning "form" or "shape".
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.
In field theory, an embedding of a field in a field is a ring homomorphism:. The kernel of is an ideal of , which cannot be the whole field , because of the condition = =. Furthermore, any field has as ideals only the zero ideal and the whole field itself (because if there is any non-zero field element in an ideal, it is invertible, showing the ...
To take the homology of a chain complex, one starts with a chain complex, which is a sequence (,) of abelian groups (whose elements are called chains) and group homomorphisms (called boundary maps) such that the composition of any two consecutive maps is zero:
In mathematics, particularly topology, the homeomorphism group of a topological space is the group consisting of all homeomorphisms from the space to itself with function composition as the group operation.