Difference between revisions of "Principal filter"
From Encyclopedia of Mathematics
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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> | + | <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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Latest revision as of 12:00, 23 November 2023
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
| [1] | Thomas Jech, Set Theory (3rd edition), Springer (2003) ISBN 3-540-44085-2 Zbl 1007.03002 |
How to Cite This Entry:
Principal filter. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Principal_filter&oldid=54591
Principal filter. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Principal_filter&oldid=54591