Category:Axioms/Filter Theory
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This category contains axioms related to Filter Theory.
Let $\struct {S, \preccurlyeq}$ be an ordered set.
A subset $\FF \subseteq S$ is called a filter of $\struct {S, \preccurlyeq}$ (or a filter on $\struct {S, \preccurlyeq}$) if and only if $\FF$ satisfies the filter axioms:
| \((1)\) | $:$ | \(\ds \FF \ne \O \) | |||||||
| \((2)\) | $:$ | \(\ds x, y \in \FF \implies \exists z \in \FF: z \preccurlyeq x, z \preccurlyeq y \) | |||||||
| \((3)\) | $:$ | \(\ds \forall x \in \FF: \forall y \in S: x \preccurlyeq y \implies y \in \FF \) |
Pages in category "Axioms/Filter Theory"
The following 2 pages are in this category, out of 2 total.