Category:Definitions/Algebras of Sets

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.