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olivier dot begassat dot cours at gmail dot com


30m
comment Definition of the triad homotopy groups
I streamlined the exposition, your original post was a little cluttered. I hope you agree with the changes. You can always edit the post to your liking.
33m
revised Definition of the triad homotopy groups
Streamlined the exposition, and highlighted the question to make it your question easier to spot.
17h
reviewed Approve suggested edit on Very basic probability problem
18h
comment The vector space $L(X,Y)$ of linear maps.
@WantTobeAbstract great!
18h
revised The vector space $L(X,Y)$ of linear maps.
added 88 characters in body
18h
answered The vector space $L(X,Y)$ of linear maps.
18h
comment The vector space $L(X,Y)$ of linear maps.
Could you try to clearly spell out your confusion? I don't understand what it is : "we want to show that $L(X,Y)$ is a linear map" just doesn't make any sense...
20h
comment The vector space $L(X,Y)$ of linear maps.
$aS+bT$ is, a priori, just a symbol assembled from two scalars and two linear maps. We want this symbol to describe a linear map $R$, so we need to specify $Rx$ for any $x\in X$. We simply define $R(x)$, for any $x\in X$, by the formula $aS(x)+bT(x)$.
Sep
14
answered Sufficient condition for $f(z)$ to be polynomial
Sep
14
comment how to prove a uniformly convex Banach space is reflexive
You should look online for course notes on functional analysis.
Sep
12
comment Why is differential geometry called differential geometry?
The fundamental theorems in differential geometry are about what the differential of a function reveals about the function's local behaviour. Integral geometry (and geometric measure theory) isn't separate from differential geometry, but it addresses different questions. It is much more about the interplay of submanifolds and measure theory, and often the differentiability assumptions are very weak.
Sep
10
reviewed Approve suggested edit on Solve equation with two unknowns
Sep
10
answered Loop spaces have the homotopy type of a topological groups
Sep
10
asked Loop spaces have the homotopy type of a topological groups
Sep
9
reviewed Close How is every subset of real numbers measurable despite the existence of a non-measurable set?
Sep
8
comment Extensions of $\mathbb{Z}_p$ by $\mathbb{Z}$ (Hilton & Stammbach III.1.2)
No problem! ${}$
Sep
8
revised Extensions of $\mathbb{Z}_p$ by $\mathbb{Z}$ (Hilton & Stammbach III.1.2)
Replaced the linked hand-drawn image with a LaTeX diagram.
Sep
8
comment Category of pointed manifolds
You don't capture the germ of a function by its differential, as witnessed by "flat functions", functions that admit a point where all its derivatives (up to any order) vanish. So I don't think you can construct a functor $G$ in the opposite direction such that $GF$ is naturally equivalent to the identity functor of $\mathbf{\mathrm{Diff}_*}$.
Sep
1
awarded  Nice Question
Aug
28
answered Are there counter intuitive interpretations of ZF or ZFC?