Oct 26, 2025 · ( This statement is important for showing equivalence of the Liu's Algebraic Geometry book's definition of open ( closed ) immersion and definition of open ( closed ) immerison in the …

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 book or …

Jun 15, 2023 · Before I can open my gym locker, I must remember the combination. Two of the numbers of this three-term sequence are 17 and 24, but I have forgotten the third, and do not know which is …

Apr 2, 2025 · In the formulation in my course notes, the codomain of the implicit function is taken to be closed. After discussing with some of my classmates, we concluded that this choice may be …

May 25, 2025 · I have proven that the compact-open topology $\tau_k$ is coarser than any topology admissible on compacta, i.e. given a topologu $\tau$ that is admissible on compacta, it follows that …

Jun 20, 2023 · I'm looking for open books on abstract algebra, other than Judson's AATA. I want one with a good number of exercises (and solutions, preferably), this one covers the rest. Does anyone …

Feb 19, 2014 · I was wondering whether I should use closed $ [-\infty, \infty ]$ or open $ (-\infty, \infty )$ notation when representing the infinity sign in interval notation.

May 19, 2025 · The latter has a "one-sidedness" condition for the elements in the open set. Previously, I thought that one could trace back to the proof of embedded submanifolds to show that such "one …

May 22, 2025 · Problem somewhat related to this post, and I refer to the same exercise in John Lee's Introduction to Smooth Manifolds. My issue is trying to understand the relationship between a …

Dec 3, 2025 · I thought that the one-point compactification of any open ball in $\mathbb {R}^n$ is homeomorphic to $S^n$ (exercise 2.7.8 in Gamelin's intro to topology). Then we can use the fact …