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olivier dot begassat dot cours at gmail dot com


Sep
19
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?
Aug
28
answered An element of $SL(2,\mathbb{R})$
Aug
24
awarded  Nice Question
Aug
21
comment What is $X^{\omega}$ where $X$ is a set?
It should be the set of sequences $(x_n)_{n\in\Bbb N}$ of elements of $X$ indexed by the nonnegative integers.
Aug
16
comment Definition of a parallelizable manifold
They surely are isomorphic as sets, but generally not as vector bundles. Parallelizability implies that there exists at least one nowhere vanishing section (actually $n$ everywhere linearly independent sections), but you will not find such a section for the 2 sphere for instance.
Aug
13
comment Continuous functions on compact Hausdorff space.
You don't need the Hausdorff property.
Aug
5
answered $SL (2, K)$ matrix conjugated by $GL(2,K)$
Aug
5
comment $SL (2, K)$ matrix conjugated by $GL(2,K)$
You will have to give us a precise statement though... Which determinant one matrices are you actually considering?