View source for Principal filter


A [[filter]] on a set $A$ consisting of all subsets of $A$ containing a given subset $X$.  If $X$ is a singleton $\{x\}$ then the principal filter on $\{x\}$ is a principal [[ultrafilter]].  The  [[Fréchet filter]] is an example of a non-principal filter.

====References====
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<TR><TD valign="top">[1]</TD> <TD valign="top">  Thomas Jech, ''Set Theory'' (3rd edition), Springer (2003) ISBN 3-540-44085-2 {{ZBL|1007.03002}}</TD></TR>
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