Julien Melleray
  • Member for 11 years, 4 months
  • Last seen more than 1 year ago
Does a power series converging everywhere on its circle of convergence define a continuous function?
Accepted answer
65 votes

I searched all over for an answer to this question back in my student days. I found the answer in a paper by Sierpinski, "Sur une série potentielle qui, étant convergente en tout point de son cercle ...

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Does the inverse function theorem hold for everywhere differentiable maps?
46 votes

For another proof that your question has a positive answer, you may look at the folowing paper by Jean Saint Raymond: http://www.math.jussieu.fr/~raymond/preprints/inversion.dvi It seems that he was ...

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Homeomorphisms and "mod finite"
10 votes

Even with a homeomorphism, preserving $=^*$ does not imply reflection. There might be an easy example, I'm not sure; at any rate it follows from a result in topological dynamics (the "absorption ...

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Borel Sets on $\mathbb{R}^n$
Accepted answer
8 votes

A way to prove it: 1/ any set of the form $A_1 \times \mathbb R \ldots \times \mathbb R$, where $A_1$ is Borel, or more generally a "Borel rectangle" with only one slice not equal to the whole space, ...

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Three questions on large simple groups and model theory
8 votes

Another rather nice example: the group of automorphisms of $[0,1]$ endowed with the Lebesgue measure (i.e, bi-measurable maps preserving the measure, identified when they coincide outside a set of ...

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Is the hyperspace of the Hilbert cube homeomorphic to the Hilbert cube
Accepted answer
7 votes

The hyperspace of any Peano continuum (locally connected metric continuum) is homeomorphic to the Hilbert cube; this is a result of Curtis and Schori, see here. I learnt about this result in a paper ...

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Start with a topological group, take the meet of the two uniformities, and take the topology. Is the result again a topological group? [xpost from math.SE]
5 votes

The meet of the left- and right- uniformities is called the Roelcke uniformity, as Todd Eisworth mentions. The topology it generates is the original topology (the same is true for the join of the two ...

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If any perfect set is uncountable in a metric space which is not complete?
5 votes

It is not so easy to construct an example of this kind, I think, because of the Hurewicz theorem: if $X$ is a coanalytic separable metrizable separable space, then either it is Polish (in particular, ...

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When do isometric actions exist?
4 votes

I got interested in a similar problem (not quite the same thing, though) a few years back but could not find anything really interesting. Here is what I found in the litterature; In case $X$ is ...

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Compactness of sigma-algebra for the $L^1$ metrics
3 votes

This space is certainly not compact in general, unless I misunderstood your question. For instance, assume the probability space in question is $[0,1]$ with Lebesgue measure. Then endow the isometry ...

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