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 …

Nov 4, 2025 · Now, my friend provided an example to show that for a union of open intervals, it is not necessarily true that the union of the boundaries of the intervals is equal to the boundary of …

Oct 5, 2025 · 0 my try Since U is open in K, it can be expressed as the intersection of some open set V in the whole space, such that U=V∩K. As U is nonempty, there exists a point x∈U. …

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 …

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. …

I was wondering whether I should use closed $ [-\infty, \infty ]$ or open $ (-\infty, \infty )$ notation when representing the infinity sign in interval notation. My teacher says to use open symbols

Aug 2, 2025 · In the particular case of the OP's question here, they've also misinterpreted the fact that center points are included in neighborhoods, so the sets can't be empty — but from my …

Apr 13, 2024 · Maybe in the second source they did not mean open or close in the subset topology? Also if all your connected components are open, you can prove that they are also …

Jul 24, 2020 · $\\newcommand{\\c}{\\mathrm{c}}$ I have already attempted the proof but I feel like there are some holes in my argument. if someone could look at it and point it out even if minor …

Sep 6, 2020 · Solution verification: Proving that a local homeomorphism maps open sets to open sets. Ask Question Asked 5 years, 2 months ago Modified 5 years, 2 months ago