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- Exact meaning of every 2d manifold is locally conformal flat
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 of Riemannian manifold, so you need to specify a Riemannian metric Amazingly, every 2-dimensional Riemannian manifold is locally conformally flat - this is the theorem you are referring to
- Two definitions of a morphism (locally) of finite type
Conversely, I do not know whether a the Stacks project's definition of a morphism of finite type (i e locally of finite type and quasi-compact) implies Hartshorne's definition of a morphism of finte type
- Unique (connected and simple) graphs that are locally prism graphs
Unique (connected and simple) graphs that are locally prism graphs Ask Question Asked 6 months ago Modified 5 months ago
- (Constructive) classification of simple, finite, locally $C_7$ graphs
I am looking for an (if possible constructive) classification of those finite, simple graphs (no loops, no multi-edges), where the open neighbourhood of each vertex (excluding that vertex aka open
- general topology - Definition of locally connected topological space . . .
A topological space is locally connected if every point admits a neighbourhood basis consisting of open connected sets To the definition given by Lee (Introduction to topological manifolds - page $92$) which sums up definitions $1$ and $2$ more "compactly" as follows;
- Terminology for local contractibility: locally contractible vs . . .
I'm working on formalizing locally contractible spaces in Mathlib (the mathematics library for the Lean theorem prover), and I've encountered conflicting terminology in the literature regarding local contractibility
- Whats stronger: projective or locally free? flat or locally free?
11 Flatness can be checked locally and free modules are flat Hence, locally free modules are flat The converse does not hold, even in the finitely generated case However, finitely presented flat modules coincide with locally free modules of finite rank Free modules are flat and direct summands of flat modules are flat
- general topology - Convexity of a connected, compact, and locally . . .
Convexity of a connected, compact, and locally convex set in $\mathbb {R}^n$ Ask Question Asked 2 years, 6 months ago Modified 1 year, 3 months ago
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