Category:Definitions/Algebras of Sets

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This category contains definitions related to Algebras of Sets.
Related results can be found in Category:Algebras of Sets.


Let $X$ be a set.

Let $\powerset X$ be the power set of $X$.

Let $\RR \subseteq \powerset X$ be a set of subsets of $X$.


Then $\RR$ is an algebra of sets over $X$ if and only if the following conditions hold:

\((\text {AS} 1)\)   $:$   Unit:    \(\ds X \in \RR \)             
\((\text {AS} 2)\)   $:$   Closure under Union:      \(\ds \forall A, B \in \RR:\) \(\ds A \cup B \in \RR \)             
\((\text {AS} 3)\)   $:$   Closure under Complement Relative to $X$:      \(\ds \forall A \in \RR:\) \(\ds \relcomp X A \in \RR \)             

Subcategories

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

Pages in category "Definitions/Algebras of Sets"

The following 5 pages are in this category, out of 5 total.