Category:Definitions/Filters on Sets
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This category contains definitions related to Filters on Sets.
Related results can be found in Category:Filters on Sets.
Let $S$ be a set.
Let $\powerset S$ denote the power set of $S$.
A set $\FF \subset \powerset S$ is a filter on $S$ if and only if $\FF$ satisfies the filter on set axioms:
\((\text F 1)\) | $:$ | \(\ds S \in \FF \) | |||||||
\((\text F 2)\) | $:$ | \(\ds \O \notin \FF \) | |||||||
\((\text F 3)\) | $:$ | \(\ds U, V \in \FF \implies U \cap V \in \FF \) | |||||||
\((\text F 4)\) | $:$ | \(\ds \forall U \in \FF: U \subseteq V \subseteq S \implies V \in \FF \) |
Pages in category "Definitions/Filters on Sets"
The following 18 pages are in this category, out of 18 total.
C
F
- Definition:Filter of Set
- Definition:Filter on Set
- Definition:Filter on Set/Also known as
- Definition:Filter on Set/Definition 1
- Definition:Filter on Set/Definition 2
- Definition:Filter on Set/Filtered Set
- Definition:Filter on Set/Trivial Filter
- Definition:Finer Filter on Set
- Definition:Finer Filter on Set/Strictly Finer