19,148 reputation
347109
bio website andrej.com
location Ljubljana
age 44
visits member for 5 years, 7 months
seen 15 hours ago
I am a professional mathematician. My area of research is logic, constructive and computable mathematics, category theory, and semantics of programming languages.

May
20
reviewed Close Copula theory on discrete random variables
May
20
reviewed Leave Open Which spaces admit bump functions?
May
18
comment Problem with a proof in Wellfounded trees in categories
You could also write an e-mail to Erik Palmgren.
May
18
comment Problem with a proof in Wellfounded trees in categories
This is just a guess, but maybe you need to use $W$-induction to simultaneously define $r$ and show that it is extensional.
Apr
28
comment Is $\textbf{FHILB}$ locally regular?
How close are we to concluding that $\mathbf{FHilb}$ is regular because it's aglebraic? (It isn't quite algebraic, but seems "mostly" so.)
Apr
18
revised Minimal totally separated spaces
editing just so I can cancel my downvote
Apr
18
comment Minimal totally separated spaces
It does not matter. There are Hausdorff spaces which match your definition ("clopens separate"), but they are not $0$-dimensional in the standard sense (i.e., small inductive dimension). Is there a standard notion of dimension for which your definitions means "$0$-dimensional"?
Apr
18
comment Minimal totally separated spaces
Ah, excellent. And so your last remark also shows that we do not even have to do anything with Stone spaces to find a counter-example: just take a totally disconnected space which is not $0$-dimensional.
Apr
18
comment Minimal totally separated spaces
Oh I see, you're saying you'll find an example which is not only totally disconnected (what OP called "0d") but is also zero-dimensional (clopens form a basis).
Apr
18
comment Minimal totally separated spaces
For small inductive dimension, zero-dimensionality is equivalent to "clopens form a basis" (see Wikipedia if you trust it, en.wikipedia.org/wiki/Zero-dimensional_space). A space is totally disconnected iff its components are singletons, see en.wikipedia.org/wiki/Totally_disconnected_space. This is equivalent to saying that every two points can be separated by a clopen, which is what you wrote.
Apr
18
comment Minimal totally separated spaces
Why are you allowed to make the assumption that the topology of $X$ is generated by the clopen sets?
Apr
18
comment Minimal totally separated spaces
Your definition of "zero-dimensional" is actually known as totally disconnected. Zero-dimensionality is usually defined as "has a basis consisting of clopen sets".
Apr
13
awarded  Nice Answer
Apr
11
comment Axiom of choice for sets of finite sets
In the formulation of $AC(Z)$ you can drop the condition $x \neq \emptyset$ as it isn't doing anything. For the empty family you always have a choice function.
Apr
1
comment Mathematicians wearing hats on arbitrary total orders
Beautiful, and with a nicely hidden use of choice in the second sentence of the proof ;-)
Mar
24
comment About the proof of the proposition “there exists irrational numbers a, b such that a^b is rational”
It is sad that this is a research-level question.
Mar
24
comment About the proof of the proposition “there exists irrational numbers a, b such that a^b is rational”
I just feel like saying $(\sqrt{2})^{\log_2 9}$. But more seriously, it is unpedagocial to speak about what we know and do not know when explaining the form of a given proof. The proof in question is not constructive because it employs the inference rule of excluded middle -- and the proof remains non-constructive no matter what else you prove or know. However, the proof can be transformed to a different proof which is constructive (assuming there is a constructive proof of irrationality of $\sqrt{2}^{\sqrt{2}}$).
Mar
12
awarded  Good Answer
Mar
12
revised What does a theoretical mathematician do?
Removing gender pronouns because someone complained about them.
Mar
9
comment A topological concept dual to compactness
Hmm, @PaulTaylor will come to the rescue here. Maybe I am mixing up external and internal definitions. In his setting we actually work internally with exponentials, so we require an "internal" right adjoint to $\Sigma^{!} : \Sigma^1 \to \Sigma^X$. This makes a difference because the said right adjoint needs to be continuous as well. Is that the problem?