Properties of Complete Boolean Algebras
- Sikorski's extension theorem states that
if A is a subalgebra of a Boolean algebra B, then any homomorphism from A to a complete Boolean algebra C can be extended to a morphism from B to C.
- Every subset of a complete Boolean algebra has a supremum, by definition; it follows that every subset also has an infimum (greatest lower bound).
- For a complete boolean algebra both infinite distributive laws hold.
- For a complete boolean algebra infinite de-Morgan's laws hold.
Read more about this topic: Complete Boolean Algebra
Famous quotes containing the words properties of, properties and/or complete:
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)
“The main reason why men and women make different aesthetic judgments is the fact that the latter, generally incapable of abstraction, only admire what meets their complete approval.”
—Franz Grillparzer (1791–1872)