Fréchet filter

The Fréchet filter (after Maurice René Fréchet ) is in the mathematics a specific amount of filters with the following definition:

It is an infinite amount. The Fréchet filter over is the set system (a set of sets, i.e. a subset of the power set of ) which contains as elements all subsets of with finite complement. ${\displaystyle X}$ ${\displaystyle X}$ ${\displaystyle X}$ ${\displaystyle X}$

Formally:

${\displaystyle {\mathcal {F}}(X)=\{\,Y\subseteq X\mid X\setminus Y{\text{ ist endlich}}\,\}}$