Marmorphism is a concept in mapping, which means that a mapping maps every element in the definition domain to an element in the value domain, that is, every element in the value domain has at least one original image.
For example, suppose there is a mapping F: A → B, where a and b are two sets respectively. If for each element B in B, there is at least one element A in A, so that f(a)=b, then this mapping F is surjective. In other words, the mapping F maps the elements in A to each element in B, and there is no element in B that has no corresponding original image.
Holotrichia is widely used in mathematics and computer science. In mathematics, surjection is an important property of function, which describes the relationship between the range of function and image set. In computer science, surjection is often used to describe some problems in mapping, relationship and programming.
Holography has many applications in mathematics:
1, function theory:
In function theory, surjection is an important function type. A surjection function is a function that maps each element in the definition domain to at least one element in the value domain. Holographic function is widely used in mathematical modeling, data analysis and image processing.
2. Algebra:
In algebra, surjectivity is an important concept of algebraic structures such as group theory and ring theory. Marmorphism plays a key role in the study of isomorphism and homomorphism of groups. The properties and structure of surjectivity are very important for solving algebraic equations and studying the isomorphic properties of algebraic structures.
3. Topological structure:
In topology, surjectivity is an important continuous mapping. Marxist plays an important role in the mapping between topological spaces, which can be used to describe the connectivity and compactness of spaces.
4, graph theory:
In graph theory, surjection is an important graph mapping. Marmorphism has important applications in isomorphic properties of graphs and coloring problems of graphs. The properties and structure of surjectivity are very helpful to solve the isomorphism and classification of graphs.