词条 | Finite character |
释义 |
In mathematics, a family of sets is of finite character provided it has the following properties:
PropertiesA family of sets of finite character enjoys the following properties:
ExampleLet V be a vector space, and let F be the family of linearly independent subsets of V. Then F is a family of finite character (because a subset X ⊆ V is linearly dependent iff X has a finite subset which is linearly dependent). Therefore, in every vector space, there exists a maximal family of linearly independent elements. As a maximal family is a vector basis, every vector space has a (possibly infinite) vector basis. {{PlanetMath attribution|id=3692|title=finite character}}{{Mathlogic-stub}} 1 : Set families |
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