Set system of finite character

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A family \mathcal{F} of sets is of finite character provided it has the following properties:

  1. For each A\in \mathcal{F}, every finite subset of A belongs to \mathcal{F}.
  2. If every finite subset of a given set A belongs to \mathcal{F}, then A belongs to \mathcal{F}.

[edit] Example

Let 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).

This article incorporates material from finite character on PlanetMath, which is licensed under the GFDL.


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