Comment by Gro-Tsen on Relation between spectra of a Cayley graph of a group...
Very nicely written and very clear, thanks!
View ArticleComment by Gro-Tsen on Removing disks with maximal radius in a disk: must the...
@JeanAbouSamra Isn't it a classic saying that the best part of emmenthal is the holes?
View ArticleComment by Gro-Tsen on Removing disks with maximal radius in a disk: must the...
I think your idea works, but it's a bit more complicated than you describe: if you just punch the $n$ circles you said in each strip, the remainder won't be nowhere dense as required. I'm fairly...
View ArticleEffective (algorithmic) computation of the moduli space of algebraic curves...
Much literature (see, e.g., references here) has been written about the existence and “construction” of moduli spaces of algebraic spaces of a given genus — coarse or fine, smooth or stable, possibly...
View ArticleComment by Gro-Tsen on Intersecting a smooth hypersurface with planes
@LorenzoAndreaus I think the results of SGA 7 exp. XVII (“Pinceaux de Lefschetz: théorème d'existence” by Katz), like thm. 2.5 and prop. 3.2 should answer your question. (Available online around here.)
View ArticleDo these nonlocal gadgets define a strict hierarchy?
Definition: For $0\leq p\leq 1$, a $p$-trigadget is a pair of boxes, each with three input buttons (say, $X,Y,Z$, only one of which can be pressed) and an light which can flash one of two colors (blue...
View ArticleComment by Gro-Tsen on Is there a topological space $X$ such that every...
① This sort of question should be posted on Math StackExchange, not MathOverflow. ② It's already answered here on Math Stackexchange (for “regular open” instead of “regular closed” but of course this...
View ArticleComment by Gro-Tsen on Cardinals arising as the real vector space dimension...
The $\lambda^{\aleph_0}$ are cardinals of uncountable cofinality which are $\geq 2^{\aleph_0}$. But are they all the cardinals of uncountable cofinality which are $\geq 2^{\aleph_0}$? I think this need...
View ArticleComment by Gro-Tsen on Points of continuity of a lower semicontinuous...
If instead of a condition on $f$ we ask for a condition on $X$, one such is discussed in this related question (there called the “super Baire” property).
View ArticleComment by Gro-Tsen on Reference request: a real-valued semicontinuous...
Sorry, maybe I wasn't clear: I wasn't asking for a proof, I have a proof, I was asking for a citeable reference.
View ArticleReference request: a real-valued semicontinuous function on a Baire space is...
I thought the following result was well-known, but I can't seem to find it in any standard textbook on real analysis or general topology:Theorem (★). Let $X$ be a Baire topological space and $f\colon...
View ArticleHow can we characterize cardinals of the form $\lambda^{\aleph_0}$?
This question is a followup to another one concerning the Hamel basis cardinalities (i.e., dimension qua vector space) of Hilbert spaces. Nik Weaver proved in an answer that they are exactly the...
View ArticleWhat does “the” mean in “the first Kleene algebra”? (In what sense is it...
Definition:“The” first Kleene algebra $\mathcal{K}_1$ is the set $\mathbb{N}$ of natural numbers endowed with the partial operation $(p,n) \mapsto p\bullet n := \varphi_p(n)$ where $\varphi_p$ is the...
View ArticleComment by Gro-Tsen on Does the decomposability of $\mathbb{R} \setminus...
To clarify the question, by $\mathbb{R}\setminus\mathbb{Q}$ you mean $\{x\in\mathbb{R}:\forall r\in\mathbb{Q}.\neg(x=r)\}$ rather than $\{x\in\mathbb{R}:\forall r\in\mathbb{Q}.(x\#r)\}$, correct? (The...
View ArticleTopological spaces in which positive and negative values of a real function...
(This question is about classical mathematics, despite the appearance of constructive mathematics terms for reasons explained below.)Definition: Say that a topological space $X$satisfies LLPO when, for...
View ArticleDoes analytic WLLPO together with sequential LLPO imply analytic LLPO?
This question is about constructive mathematics, without any form of Choice except Unique Choice, such as in the internal logic of a topos with natural numbers object, or in IZF. The “reals” (and the...
View ArticleAnswer by Gro-Tsen for What to do if paper was rejected with good report?
This happened to me once, and the editor of the editor whose editorial board took the decision to reject the paper offered to disclose the referee's identity to another journal if I chose to resubmit...
View ArticleComment by Gro-Tsen on Is every real number the limit of a sequence of...
You've interpreted $\mathbb{R}\setminus\mathbb{Q}$ as $\{x\in\mathbb{R}:\forall y\in\mathbb{Q}.(x\#y)\}$ but OP meant it as $\{x\in\mathbb{R}:\forall y\in\mathbb{Q}.\neg(x=y)\}$. The former is...
View ArticleComment by Gro-Tsen on Is every real number the limit of a sequence of...
@MikhailKatz The problem is that, in constructive math in the absence of Choice, one cannot assert that every (Dedekind) real number is the limit of a sequence of rationals: those that are are the...
View ArticleComment by Gro-Tsen on Is every real number the limit of a sequence of...
Aw, you beat me to it. 😖
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