Definition:Filter in Ordered Set
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May 6, 2023: It has been suggested that this page or section be merged into Definition:Filter. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Mergeto}} from the code. |
Definition
Let $\struct {S, \preceq}$ be a preordered set.
Let $F$ be a subset of $S$.
$F$ is a filter in $\struct {S, \preceq}$ if and only if:
Sources
- 1980: G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove and D.S. Scott: A Compendium of Continuous Lattices
- Mizar article WAYBEL_0:mode 4