# Category:Definitions/Minimally Closed Classes

This category contains definitions related to Minimally Closed Classes.
Related results can be found in Category:Minimally Closed Classes.

Let $A$ be a class.

Let $g: A \to A$ be a mapping.

### Definition 1

$A$ is minimally closed under $g$ with respect to $b$ if and only if:

 $(1)$ $:$ $A$ is closed under $g$ $(2)$ $:$ There exists $b \in A$ such that no proper subclass of $A$ containing $b$ is closed under $g$.

### Definition 2

$A$ is minimally closed under $g$ with respect to $b$ if and only if:

 $(1)$ $:$ $A$ is closed under $g$ $(2)$ $:$ There exists $b \in A$ such that every subclass of $A$ containing $b$ which is closed under $g$ contains all the elements of $A$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Definitions/Minimally Closed Classes"

The following 3 pages are in this category, out of 3 total.