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Results tagged with boolean-algebras
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user 402
A Boolean algebra is a commutative ring satisfying x²=x for every x, and sometimes required to have a unit; they have characteristic 2. For coding theory (notably dealing with subsets linear subspaces of spaces of Boolean functions), rather use the [coding-theory] or [linear-algebra] tag.
7
votes
Analytical origins of the Stone duality
Stone himself gave a brief account of his discovery of Stone duality in a letter written in 1976.
Apparently, von Neumann was involved.
A reminiscence on the extension of the Weierstrass approximation …
- 37.8k
10
votes
Analytical origins of the Stone duality
In addition to the historical component, the question also asked about the relation between spectral theory and Stone spaces.
$\def\Z{{\bf Z}} \def\R{{\bf R}} \def\C{{\bf C}} \def\Spec{\mathop{\rm Spe …
- 37.8k
7
votes
Is the Pierce spectrum useful elsewhere in Mathematics?
For Boolean rings, the Pierce spectrum coincides with the Zariski spectrum
and is one of the functors implementing the
Stone duality between Boolean algebras and compact
totally disconnected Hausdorff …
- 37.8k
4
votes
Accepted
Star-autonomous categories are categorifications of Boolean algebras?
The starting point for decategorification is the observation that a category in which any parallel arrows are equal must necessarily be a preorder.
Restricting to skeletal categories makes it a poset. …
- 37.8k
12
votes
Accepted
Which sigma-ideals in a sigma-algebra are ideals of null sets?
First of all, one should mention that not every triple (X,B,μ) (i.e., what is often called a measure space)
satisfies the property that its C*-algebra of bounded functions is a von Neumann algebra (= …
- 37.8k
2
votes
Accepted
Continuous surjection between spectra of commutative von Neumann algebras
Is it true that π maps clopen sets into clopen sets?
This is true if and only if the inclusion $V_1→V_2$ is a morphism of von Neumann algebras, i.e., its image is closed in the ultraweak topology.
S …
- 37.8k
21
votes
1
answer
1k
views
Which complete Boolean algebras arise as the algebras of projections of commutative von Neum...
Projections in an arbitrary commutative von Neumann algebra form a complete Boolean algebra.
Moreover, a morphism of commutative von Neumann algebras induces
a continuous morphism of the corresponding …
- 37.8k