# finitely generated

> English word · Adjective

## Definitions
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:
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:
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:
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:
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:

## Etymology
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.

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/finitely-generated