complex analysis - Locally uniform convergence of given series ...
Apr 12, 2024 · Ok so just for short clarification: You are using this criterion for uniform convergence, but instead of uniform convergence of the series of differences, you show locally uniform convergence. …
algebraic topology - locally simply-connected vs. semilocally simply ...
Jul 20, 2017 · Can someone help me understand the difference between locally simply-connected and semilocally simply-connected? I actually need more help understanding (with an example), what it …
The definition of locally Lipschitz - Mathematics Stack Exchange
Here's a scan of the first edition of the text, where the only change from the second (latest) edition referred to above is that the last sentence now reads "This is called the local Lipschitz property" …
Locally Principal Ideal Domain - Mathematics Stack Exchange
Sep 7, 2020 · Locally Principal Ideal Domain [duplicate] Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago
general topology - Reasoning for definition of locally homeomorphic ...
Aug 22, 2017 · For example, the circle is locally homeomorphic to $\mathbb {R}$, but there is no local homeomorphism from the circle to the real line - for any such map, at some point the path needs to …
Locally convex implies convex? - Mathematics Stack Exchange
Dec 24, 2020 · In other words, Ω Ω is uniformly locally convex. Recall open connected implies path connected and Ω ∩Ux¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯ Ω ∩ U x is convex, so Ω¯¯¯¯ Ω is path connected (this is …
Hereditarily locally connected spaces - Mathematics Stack Exchange
Jul 29, 2025 · Here, a space is called hereditarily locally connected ("hlc"), if each subset is locally connected. Note that this is much stronger than the usual definition, which requires only …
Localization of locally compact commutative ring
May 7, 2024 · If A A is a locally compact (Hausdorff) commutative ring and S S is a multiplicatively closed subset of A A, is there any natural topology we can put on AS−1 A S 1 such that it also …
algebraic geometry - Constant sheaf vs locally constant sheaf ...
Apr 20, 2020 · This is supposedly locally a constant sheaf but not a constant sheaf. But by definition of the constant sheaf, we have that this sheaf is constant on connected components as it is constant on …
Define a topology of locally uniform convergence on $Y^X$
Jan 10, 2022 · In case X is locally compact Hausdorff, then compact convergence is equivalent to local uniform convergence, so one can use the co-topology. But in general I guess the topology should be …