Set system of finite character
- Set system of finite character
A family of sets is of finite character provided it has the following properties:
#For each , every finite subset of belongs to
#If every finite subset of a given set belongs to , then belongs to
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). ----
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