# Fréchet filter

From Encyclopedia of Mathematics

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The filter on an infinite set $A$ consisting of all cofinite subsets of $A$: that is, all subsets of $A$ such that the relative complement is finite. More generally, the filter on a set $A$ of cardinality $\mathfrak{a}$ consisting of all subsets of $A$ with relative complement of cardinality strictly less than $\mathfrak{a}$. The Fréchet filter is not principal.

The *Fréchet ideal* is the ideal dual to the Fréchet filter: it is the collection of all finite subsets of $A$, or all subsets of cardinality strictly less than $\mathfrak{a}$, respectively.

#### References

[1] | Thomas Jech, Set Theory (3rd edition), Springer (2003) ISBN 3-540-44085-2 Zbl 1007.03002 |

**How to Cite This Entry:**

Fréchet ideal.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Fr%C3%A9chet_ideal&oldid=39486