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I am a professor of Mathematics at the University of Pisa, Italy.


19h
comment Two questions on hyperspace of a metric space
As to the first question, you may also observe that if $(X,d)$ is a compact metric space, its hyperspace $H(X)$ (the set of closed sets of $X$ endowed with the Hausdorff distance) is a compact metric space too; moreover the construction extends to a functor from the category of compact metric spaces & continuous functions into itself, precisely : if $f:X\to Y$ is continuous the map $K\to f(K)$ is continuous from $H(X)$ to $H(Y)$ (just because $f$ is uniformly continuous). In particular, if $(X,d)$ and $(X',d')$ are homeomorphic compact metric spaces, so are their hyperspaces.
2d
awarded  Good Answer
Apr
22
revised Functional minimization problem
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Apr
21
answered Functional minimization problem
Apr
20
comment Boundary Value System.
Besides, the set of solutions of that ODE is a 2n linear space; the given BVC can't identify any.
Apr
20
comment Boundary Value System.
And if $A=B$, $y(x)$ does not depend on $x$?
Apr
18
revised Biggest parallelogram inside the union of two translated parallelograms
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Apr
18
revised Biggest parallelogram inside the union of two translated parallelograms
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Apr
18
comment Biggest parallelogram inside the union of two translated parallelograms
Even larger than the area of the parallelogram \ \ with the lower horizontal edge moved to the right (therefore, not the green one // ) ?
Apr
18
revised Biggest parallelogram inside the union of two translated parallelograms
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Apr
18
revised Biggest parallelogram inside the union of two translated parallelograms
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Apr
18
answered Biggest parallelogram inside the union of two translated parallelograms
Apr
17
comment Biggest parallelogram inside the union of two translated parallelograms
Since linear maps preserves ratios of measures, it may be assumed wlog that the two parallelograms are squares. This simplifies the problem...
Apr
16
comment Old Peano theorem (demonstration is missing details)
It seems to me that the computation in the linked book ("Geometric applications of differential calculus") is clear and rigorous, as in Peano's style. Of course, a reader of a textbook is supposed to start from the beginning, so I suppose you need to refer to the material in the previous part of this textbook in order that notations, definitions and properties used are clear.
Apr
16
comment Fair cake-cutting between groups
A remark on the existence result. Even with $k$ states and $N$ atomless probability measures, there exists a measurable $k$-partition $\{A_j\}_{1\le j\le k}$ such that $\mu_i(A_j)=1/k$ for all $1\le i\le N$ and $1\le j\le k$. It's a consequence of the Lyapounov convexity theorem.
Apr
11
comment Invariant mesures for expanding maps of the circle
I don't understand... how can $T:\mathbb{S}^1\to \mathbb{S}^1$ have $T'(x)>1$ for all $x$ ?
Apr
6
comment Between Tietze's and Dugundji's Extension Theorems
@Włodzimierz Holsztyński. Sorry, I will not.
Apr
5
comment Between Tietze's and Dugundji's Extension Theorems
@Włodzimierz Holsztyński: thank you for your comment. However, the question is not about the original author of (what is known as) Tietze theorem. As you probably know, most theorems are known after a name which is different from the person who discovered it; often by the author's choice. en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy
Apr
3
comment Between Tietze's and Dugundji's Extension Theorems
Thank you very much. Would you write this as an answer, possibly with some details, or a reference?
Apr
3
comment Between Tietze's and Dugundji's Extension Theorems
And I think at least in the case of a separable $E$, one can pass from a linear extensor for the scalar case to one for E-valued mappings, by the argument in Bill Johnson's answer.