the equivalence of two definitions of locally closed sets
Oct 24, 2025 · here there are 2 definitions of locally closed sets: A A is locally closed subset of X X if: a) every element in A A has a neighborhood V V in X X such that A ∩ V A ∩ V is closed in …
'Locally' Convex Function - Mathematics Stack Exchange
Jun 2, 2020 · My question is a rather basic one, can we establish that local convexity of this kind implies global convexity? Are any extra conditions needed? My intuition suggests that a …
Injective morphisms of locally free sheaves and fiberwise injectivity ...
The transition between locally free sheaves and vector bundles is functorial and it is actually an equivalence of categories. Now assume that φ: E → H φ: E → H is an injective morphism …
Locally closed subspace - Mathematics Stack Exchange
Aug 19, 2020 · Locally closed subspace Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago
algebraic geometry - Constant sheaf vs locally constant sheaf ...
Apr 20, 2020 · 7 I'm getting very confused distinguishing the difference between a locally constant sheaf and a constant sheaf. $\textbf {Constant sheaf}$: Let M be a vector space.
Exact meaning of "every 2d manifold is locally conformal flat"
May 5, 2025 · The definition is given in the third paragraph on the Wikipedia article (also see the following paragraph for differences in naming). Note that local conformal flatness is a property …
Locally compact valued field is complete? - Mathematics Stack …
Sep 29, 2017 · In J. P. Serre's book Local Fields, in the proof of one proposition it says: If K K is locally compact, it is complete. How did he deduce that? As far as I know, there is no …
general topology - When is a Borel measure locally finite ...
Feb 6, 2023 · Clearly locally finite measures are Borel. And if E E is also locally compact (i.e., every x ∈ E x ∈ E has a neighborhood U ∋ x U ∋ x for which U¯¯¯¯ U is compact), then clearly …
abstract algebra - Locally Noetherian schemes are quasiseparated ...
Sep 26, 2020 · Locally Noetherian schemes are quasiseparated Ask Question Asked 5 years, 3 months ago Modified 5 years, 3 months ago
functional analysis - What is Convex about Locally Convex Spaces ...
A locally convex TVS is one that has a basis at the origin consisting of balanced absorbing convex sets. The reason for the emphasis on "convex" is that that's what distinguishes locally convex …