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visits member for 3 years, 8 months
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Jun
29
comment Naive definition of surface area doesn't work?
Perhaps one needs to add that the vertical and the horizontal legs tend to zero "uniformly" in some sense... Where is this written?
Jun
29
comment Naive definition of surface area doesn't work?
@BenoîtKloeckner, as far as I understand it is sufficient to claim that the corresponding triangles in the set of parameters are right (i.e. one of their angles is right) and their legs are parallel to the coordinate lines. Is it true?
Jun
20
comment Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Federico, as far as I understand, the problem with the equivalence of these two axioms arises when we define polytopes as compact sets (spanned by... etc), then $P\setminus Q$ needs not to be a polytope, and the functional $V_n$ is not defined on $P\setminus Q$.
Jun
20
comment Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Even for the dimension $n=3$ this trick becomes bulky. To say nothing about $n>3$. Or I don't know something? Anyway this looks like a new invention of bicycle. It's difficult to believe that nobody did this before.
Jun
20
comment Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Thank you, Liviu. I am reading this.
Jun
20
comment Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Is it possible that this wasn't proved in textbooks?
Jun
20
comment Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Eric, I don't understand. Do you mean that for proving this it is nesessary to extend $V_n$ to the Jordan (or Lebesgue) measure (and only after that this becomes evident)? I believe there is a simple trick that allows to prove this without going to Jordan.
Jun
20
comment Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
I meant, disappeared from the list of the questions on the main page. I thought, this means that nobody is interested.
Jun
20
comment Axiomatic explanation of why the volume of a parallelepiped is equal to the area of its base times its height
Perhaps, this is my bad English. What is it called when something appears and disappears immediately?
May
23
comment Correspondence between real forms and real structures on complex Lie groups
@MikhailBorovoi, excuse me, I did not understand, for which class of groups this is a one-to-one correspondence? And is this a folklore, or there exist references?
May
22
comment Correspondence between real forms and real structures on complex Lie groups
@YCor: Yes, I thought the same, an involutive anti-linear Lie algebra automorphism. So this is not a one-to-one correspondence?... I think, at least for reductive groups (i.e. for complexifications of compact real Lie groups) this must be so... That's true?
May
22
comment Correspondence between real forms and real structures on complex Lie groups
@YCor: Pardon, I corrected the text in MSE (and here also).
May
22
comment Correspondence between real forms and real structures on complex Lie groups
Does this give an answer in the case, when $K$ is a compact real Lie group and $G$ is its complexification?
May
4
comment Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
Gérard, as far as I understand, the exponential map of $\text{Diff}({\mathbb T})$ is also not locally invertible. I think, you should accept Alexander Schmeding's answer, it sounds much more useful.
May
4
comment Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
@YCor, I thought this means that there is a neighbourhood $U$ of 1 in $G$, and a neighbourhood $V$ of 0 in $L(G)$ such that $\exp(V)=U$.
May
4
comment Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
Gérard, the Lie algebra for ${\mathbb T}^{\mathfrak m}$ is ${\mathbb R}^{\mathfrak m}$, the ${\mathfrak m}$-th power of $\mathbb R$.
May
4
comment Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
Gérard, some infinite dimensional locally compact groups have exponential maps that are surjective. For example, the infinite power ${\mathbb T}^{\mathfrak m}$ (where ${\mathfrak m}$ is any infinite cardinal) of the circle $\mathbb T$ has this property.
Apr
24
comment Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
Will it be correct to reformulate your question as follows: when is the exponential map $\exp:L(G)\to G$ (locally) surjective?
Apr
19
comment Quantum mechanics formalism and C*-algebras
I bet, $F^*$-algebras will not save quantum mechanics, but stereotype ones will do: arxiv.org/abs/1303.2424 :)
Mar
23
comment What are the applications of operator algebras to other areas?
Sébastien, the problem exists. Not only in this concrete field, but in many fields in mathematics. You were right when asking this question, this is a normal reaction of a human (contrary to robot). The discussions like this must be common in science, otherwise this activity turns into a religion (where references to "tone" replace doubts :).