Oct 5, 2011 · Is there a listing of open problems in math? Let me make myself clearer. I'm a grad student and I want to train my abilities with not yet solved problems. So is there a list, or a …

Q&A for people studying math at any level and professionals in related fields

Dec 14, 2025 · My question is this. Is there a semi-open set which is not open in $\mathbb {R}_\ell$? My attempt was at the intervals $ (a,b]$ and $ [a,b]$ because these intervals are not …

Dec 11, 2025 · In my intro alg. geo class, o so many years ago, the prof recounted how the influential algebraic geometer Solomon Lefschetz, having since changed his field of study …

Apr 15, 2021 · This characterization works well for intervals because they are convex (notice the demo uses midpoint), but it's not much different for general open sets in $\mathbb R^n$. See …

Jan 22, 2015 · 2 'Not closed' does not mean open, for example the set $ [0,1)$ is neither open nor closed. And, as you suggest, sets can be both open and closed (as both $\varnothing$ and …

Task Let $M$, $N$ be smooth manifolds of dimension $m$ and $n$ respectively and $f\colon M\longrightarrow N$ a submersion. Show that $f$ is open. My Proof Let $W\subset M$ be …

I'm interested in finding a math-related open source project that I can contribute to. I've studied maths and stats at undergraduate level, but I'm a professional software developer and I'll have …

Dec 24, 2020 · My differential geometry professor said that the tangent space of an open set Ω Ω of Rn R n at a point P P coincides with Rn R n , that is TP(Ω) =Rn T P (Ω) = R n He gave an …

Dec 20, 2014 · 9 I'm confused by the proof that $\epsilon$-$\delta$ continuity is equivalent to open-set continuity. One can prove that a function is $\epsilon$-$\delta$-continuous if and only …