finitely generated

短语

别名

f.g.

释义与例句

adj.
  1. 1.

    In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:

    Such that the functor operatorname Hom_( mathcal )C(X,·) preserves those filtered colimits of monomorphisms.

    数学 计算机 工程
  2. 2.

    In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:

    Being a quotient object of a free object over a finite set, i.e. being the target of a regular epimorphism from an object which is free on a finite set.

    数学
  3. 3.

    In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:

    Having a finite set of generators, i.e. having a finite set of elements from which all other elements can be created in finitely many steps under the permitted operations (viz. the group operation for groups, addition and scalar multiplication for modules, addition and multiplication for rings, etc.)

    数学
  4. 4.

    In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:

    Finitely generated as a (left) module over R.

    数学
  5. 5.

    In any of several specific senses, such that all its elements can be created using (or described by reference to) a finite set of elements, usually called generators:

    Equipped with an Alexandrov topology (i.e. one where the intersection of every family of open sets is open).

    数学

词源

From the study of generators. The motivation for calling topologies satisfying sense 1.5 "finitely generated" is that any topology satisfies sense 1.5 if and only if it is coherent with its finite subspaces. Thus, metaphorically, it is "generated" by them. The category-theoretic senses were created to generalize those of abstract algebra, and so were named identically.

来源：wiktionary