Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with boolean-algebras
Search options not deleted
user 5903
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.
5
votes
Accepted
Stone-Čech compactification of a Boolean subalgebra of $\{0,1\}^S$
A partial answer.
for your specific example, the algebra $B$ generated by the rational intervals, the answer is negative. This algebra is countable and dense in $2^\mathbb{R}$. It is countable and ze …
- 32.5k
9
votes
Accepted
A strictly descending chain of subalgebras of $P(\omega)/_{\mathrm{fin}}$
There is a family $\{K_X:X\subseteq\mathfrak{c}\}$ of separable compact
zero-dimensional spaces such that there is a continuous surjection of $K_X$
onto $K_Y$ if and only if $X\subseteq Y$.
These spac …
- 11.4k
4
votes
Accepted
Copy of $P(\omega)/\mathrm{fin}$ on $\omega_1$
To expand my comment into an answer: take, for each $n\in\omega$, a uniform ultrafilter $u_n$ on $\omega_1$ that contains the set $\{\lambda+n:\lambda$ is a limit or $0\}$.
The set $U=\{u_n:n\in\omega …
- 11.4k
2
votes
Accepted
Complete CCC Boolean algebras (or Stonean spaces)
A partial answer to the question about the Gleason cover of the unit interval: it can be found everywhere in every compact extremally disconnected space.
The point is: in a compact extremally disconne …
- 11.4k
2
votes
Accepted
Description of atomless complete Boolean algebras with a countable $\pi$-base
To make the answers concrete: the Boolean algebra of clopen subsets of the Cantor set is the unique countable atomless Boolean algebra.
Its completion is the regular-open algebra of the Cantor set, wh …
- 11.4k
7
votes
Accepted
Can any poset of cardinality $\leq 2^{\aleph_0}$ be embedded in ${\cal P}(\omega)/(\text{fin...
Here is an attempt at a 'definitive summary'.
To begin with positive results: $\mathsf{CH}$ implies a “yes” answer to
this question. The fastest way to see this is to first embed a given partial
order …
- 11.4k
4
votes
Accepted
Extremally disconnected rigid infinite Hausdorff compacta(?)
This paper, Rigid Stone spaces within $\mathsf{ZFC}$ by Dow, Gubbi, and Szymański contains relatively easy examples of such spaces.
- 11.4k
5
votes
Accepted
A problem of non-emptiness of intersections of certain chains of regular open sets
Here is a provisional negative answer.
If $\mathcal{C}$ is a c-minimal chain then $N=\bigcap\mathcal{C}$ is closed and nowhere dense (if nonempty): if the interior is nonempty take a nonempty regular …
- 11.4k
5
votes
Self-homeomorphism of Stone-Čech boundary with an isolated fixed point
As an answer to the bonus question: no, see K. P. Hart and J. Vermeer. Fixed-point sets of autohomeomorphisms of compact F-spaces,
Proceedings of the American Mathematical Society, 123 (1995), 311–314 …
- 11.4k
2
votes
Can this ultrafilter convergence condition be expressed as a compactness condition?
Your condition amounts to saying that the uniformity $\mathcal{C}$ generated by all clopen partitions is complete: 'partition-prime' is the same as '$\mathcal{C}$-Cauchy'.
It is also implied by the co …
- 11.4k
6
votes
A unique ultrafilter extending a union of filters?
The following is due to Alan Dow:
In any model obtained by adding $\aleph_2$ many Cohen reals to a model
of $\mathsf{CH}$ the statement is false.
We force with $\mathbb{P}=\operatorname{Fn}(\omega_2, …
- 11.4k
16
votes
Accepted
Is Stone-Čech compactification of 0-dimensional space also 0-dimensional?
In this paper (Spaces $N\cup\mathscr{R}$ and their dimensions, Topol. Appl.
11(1) 1980 93-102) — I hope the PDF is freely available) Jun Terasawa constructs maximal almost disjoint families on $\mathb …
- 63.9k
3
votes
Ideals on $\mathbb N$ and large sets that have small intersection
In topological language: for any closed subset, $F$, of $\beta\mathbb{N}\setminus\mathbb{N}$ the family $I_F=\{A:A^*\cap F=\emptyset\}$ is an ideal.
Your property translates into: the closed set $F$ i …
- 11.4k
1
vote
About the existence of a particular kind of "splitting" function on atomless complete Boolea...
I think you are asking too much.
Assume we have such a function and let $a$ be nonzero such that both $a_0$ and $a_1$ are nonzero. Then $b\le a_0$ implies $b_1=0$ and $b\le a_1$ implies $b_0=0$.
If …
- 11.4k
6
votes
Accepted
Can the Boolean Algebra of regular open sets be isomorphic to ${\cal P}(\omega)/(\text{fin})$?
No, $\mathrm{RO}(X)$ is complete; $\mathcal{P}(\omega)/\mathit{fin}$ is not (no strictly increasing sequence has a supremum).
- 11.4k