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 posets
Search options not deleted
user 5903
A poset or partially ordered set is a set endowed with a partial order, meaning a binary relation $\leq$ which is reflexive ($x \leq x$ for all $x$), antisymmetric ($x\leq y$ and $y\leq x$ implies $x=y$), and transitive ($x\leq y$ and $y\leq z$ implies $x \leq z$).
6
votes
Surjective order-preserving map $f:{\cal P}(X)\to \text{Part}(X)$
The positive solution uses an equivalent of the Axiom of Choice:
for every infinite set $A$ there is a bijection $f:A\to A\times A$.
In the basic Fraenkel Model (section 4.3 in Jech's Axiom of Choice …
- 11.4k
1
vote
Accepted
Partial orders on downward closed sets
Conditions 4 and 5 show that $(\mathfrak{D}(P),{\subseteq})$ satisfies condition 2 in the list: because $V\in\mathfrak{D}(P)$ we have the second part of 2; and 5 says that $(\mathfrak{D}(P),{\subseteq …
- 11.4k
7
votes
Accepted
Embedding ordinals with the order topology into connected $T_2$-spaces
The answer is no: if $\lambda$ is larger than $\omega^2$ and if $X$ contains $\lambda+\omega$ then it also contains $\lambda+\omega+\omega$.
To see this observe that $\lambda+1$ is homeomorphic with $ …
- 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