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 Yearling
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Feb
1
comment Uppercase E notation for sets?
An 'E' with brackets commonly denotes an expected value, as from probability theory. Given that they are writing a $u$ in the subscript, they could be defining $L_i$ to be the expected value of $u$ over some event, and similarly for $K$.
Jan
27
comment uncountable co-meagre set in Polish Spaces
Aha! I believe the theorem is true for Polish spaces $X$ with no isolated points, though.
Jan
26
comment uncountable co-meagre set in Polish Spaces
You might look at the Baire category theorem.
Jan
26
revised uncountable co-meagre set in Polish Spaces
Changed "infinite" to "uncountable" to make the question correct.
Jan
26
suggested approved edit on uncountable co-meagre set in Polish Spaces
Jan
26
comment uncountable co-meagre set in Polish Spaces
As for the question, do you know any major theorems about meager subsets of uncountable Polish spaces?
Jan
26
comment uncountable co-meagre set in Polish Spaces
$X = \mathbb{N}$ is an infinite Polish space, and every subset of it is countable. I think you mean that $X$ should be uncountable itself.
Jan
22
comment Finding all metrics of set $X=\{1,2,3\}$
You're right that for any metric $d$, a scaling of $d$ by a positive constant is also a metric, so there are infinitely many. I think the point of the question is that you can list them all using only finitely many constants.
Jan
22
answered Clopen subspaces of Stonean spaces
Jan
20
comment How can it be seen that the Von Neumann universe $V_{\omega+\omega}$ does not model the Fraenkel axiom
Thanks Asaf, I knew I was saying something wrong, but I posted anyway. At least now we have some more interesting stuff written here.
Jan
20
revised How can it be seen that the Von Neumann universe $V_{\omega+\omega}$ does not model the Fraenkel axiom
pointed out a false thing.
Jan
20
answered How can it be seen that the Von Neumann universe $V_{\omega+\omega}$ does not model the Fraenkel axiom
Jan
20
comment How can it be seen that the Von Neumann universe $V_{\omega+\omega}$ does not model the Fraenkel axiom
Look at the function $f : \omega \to \omega + \omega$ defined by $f(n) = \omega + n$.
Jan
7
answered There is no Baire bijection between $\mathbb R$ and the set of functions $\mathbb Z\to\mathbb R$ modulo shifts
Dec
22
awarded  Yearling
Nov
7
awarded  Nice Answer
Sep
15
comment Cardinality of $Def(X)$
Choice probably only appears in showing that the set of finite tuples $(x_0,\ldots,x_m)$ from $M$ has the same cardinality as $M$.
Sep
5
comment Every $f\in\omega^\omega$ is bounded by the “increasing enumeration” of the intersection of a countable dense set and a dense open set in $\mathbb{R}$
I'm confused. Isn't it true that if $Y$ and $Z$ are subsets of $X$ and $Y\subseteq Z$, then $f_Z \le f_Y$? Then letting $U_n$ ($n < \omega$) be a countable base for $\mathbb{R}$, we have for every open $V$ that there exists an $n$ such that $f_{V\cap X} \le f_{U_n\cap X}$. Then letting $g$ be a $<^*$-bound on the functions $f_{U_n\cap X}$, we have $f_{V\cap X} <^* g$ for all open $V$.
Sep
2
comment Limiting the size of near-coherence classes in $\omega^*$
It's pretty standard, Asaf.
Aug
23
answered extending automorphisms in complete boolean algebras