Category:Definitions/Minimally Closed Classes

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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.