# 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 only the following subcategory.

## Pages in category "Choice Functions"

The following 15 pages are in this category, out of 15 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

### 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