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.