Category:Rings of Sets

From ProofWiki
Jump to navigation Jump to search

This category contains results about Rings of Sets.
Definitions specific to this category can be found in Definitions/Rings of Sets.


A ring of sets $\RR$ is a system of sets with the following properties:

\((\text {RS} 1_1)\)   $:$   Non-Empty:    \(\displaystyle \RR \ne \O \)             
\((\text {RS} 2_1)\)   $:$   Closure under Intersection:      \(\displaystyle \forall A, B \in \RR:\) \(\displaystyle A \cap B \in \RR \)             
\((\text {RS} 3_1)\)   $:$   Closure under Symmetric Difference:      \(\displaystyle \forall A, B \in \RR:\) \(\displaystyle A * B \in \RR \)             

Subcategories

This category has the following 2 subcategories, out of 2 total.

A

S