Difference between revisions of "User:Alec/Manifolds pages"

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Manifolds Definitions

Manifolds Notes

Smooth Manifolds

Topological Manifolds

Algebra (disambiguation)

Algebra (linear algebra)

Class of smooth real-valued functions on R-n

Class of smooth real-valued functions on R-n/Structure

Classes of continuously differentiable functions

Deformation retract

Differentiability

Differential of a smooth map

Differentiation

Given a topological manifold of dimension 2 or more and points p1, p2 and q where q is neither p1 nor p2 then a path from p1 to p2 is path-homotopic to a path that doesn't go through q

Graph (topological manifold)

If two charts are smoothly compatible with an atlas then they are smothly compatible with each other

Kronecker delta

Locally euclidean

Locally euclidean of dimension n

Locally Euclidean of dimension n

Locally euclidean topological space

Locally Euclidean topological space

Locally Euclidean topological space of dimension n

Motivation for smooth manifolds

Motivation for smooth structures

Motivation for tangent space

Motivation for tangent space definitions

Orientable surface

Real projective space

Real-valued function

Set of all derivations at a point

Set of all derivations of a germ at a point

Smooth function

Smooth manifold

Smooth structure

Smoothly compatible charts

Sphere (topological manifold)

Standard coordinates

Strong deformation retract

The set of all germs of smooth functions at a point

Topological manifold

Topological retraction

Topological retraction/Definition

Types of topological retractions

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