Category:Choice Functions
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This category contains results about Choice Functions.
Definitions specific to this category can be found in Definitions/Choice Functions.
Let $\mathbb S$ be a set of sets such that:
- $\forall S \in \mathbb S: S \ne \O$
that is, none of the sets in $\mathbb S$ may be empty.
A choice function on $\mathbb S$ is a mapping $f: \mathbb S \to \ds \bigcup \mathbb S$ satisfying:
- $\forall S \in \mathbb S: \map f S \in S$
That is, for a given set in $\mathbb S$, a choice function selects an element from that set.
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Choice Functions"
The following 17 pages are in this category, out of 17 total.
C
- Choice Function Exists for Set of Well-Ordered Sets
- Choice Function Exists for Well-Orderable Union of Sets
- Choice Function for Power Set implies Choice Function for Set
- Choice Function for Set does not imply Choice Function for Union of Set
- Closed Set under Chain Unions with Choice Function is of Type M
- Closure under Chain Unions with Choice Function implies Elements with no Immediate Extension
- Countable Set has Choice Function
E
S
- Set of Finite Character with Choice Function is of Type M
- Set of Finite Character with Choice Function is Type M
- Set of Finite Character with Countable Union is Type M
- Set of Subsets of Finite Character of Countable Set is of Type M
- Set with Choice Function is Well-Orderable
- Swelled Set which is Closed under Chain Unions with Choice Function is Type M