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visits member for 4 years, 7 months
seen Dec 16 at 19:52

Dec
10
comment Infinite topological spaces such that every subset is a retract
"finite chain, $\mathbb{N}$, $-\mathbb{N}$, or" $\:$ can be replaced with $\:$ "connected subspace of"$\:$. $\;\;\;\;$
Dec
3
comment Hausdorff spaces with trivial automorphism group
The empty space is another example. $\;$
Nov
16
comment Infinite matrices with a finite number of non-zero values on each row
@AlexDegtyarev: $\:$ That be for "a finite number of non-zero values on each" column. $\hspace{1.34 in}$
Nov
3
awarded  Nice Question
Oct
15
comment Is it possible to formulate the axiom of choice as the existence of a survival strategy?
The argument is somewhat tricky, but I think it's also the case that if the giraffes form a strictly amorphous set (i.e., for all partitions of them, at most one piece is infinite and at most finitely many pieces have more than one element), then they have a winning strategy in the case that there are the same number of colors as giraffes. $\;$
Oct
14
comment Is it possible to formulate the axiom of choice as the existence of a survival strategy?
This paper shows that it is even consistent with $\:$ZF+DC($\omega_1\hspace{-0.03 in}$)$\:$ that every set of reals has Baire property. $\hspace{.25 in}$
Oct
10
revised Motion planning algorithm
improved grammar
Oct
8
comment How to generalize balanced and absorbing sets to R-modules?
One can generalize "balanced" and "absorbing" to bornological rings. $\;$
Oct
5
comment Combinatorial optimization problem involving infinite spin system
Should the lim be replaced with limsup? $\;\;\;$ If no, should $S$ be defined as $\{\phi \in \{\hspace{-0.02 in}0\hspace{.02 in},\hspace{-0.04 in}1\hspace{-0.03 in}\}^{\mathbb Z} : \text{ the following limit exists}\}\:$ and $\:\{\hspace{-0.02 in}0\hspace{.02 in},\hspace{-0.04 in}1\hspace{-0.03 in}\}^{\hspace{-0.02 in}\mathbb Z}\:$ be replaced with $S\hspace{.02 in}$? $\hspace{1.7 in}$
Sep
30
accepted Does the implicit function theorem hold for discontinuously differentiable functions?
Sep
30
comment Does the implicit function theorem hold for discontinuously differentiable functions?
Oh. $\:$ I misread your middle paragraph, and thought you were doing this without assuming $\hspace{.46 in}$ differentiability of $\hspace{.04 in}f$ with respect to its $\mathbb{R}^n$ argument. $\;\;\;\;$
Sep
29
comment Does the implicit function theorem hold for discontinuously differentiable functions?
Is "it" the theorem or the proof? $\:$ If "it" is the theorem, then one would need to derive a local lower bound on the size of the neighborhoods $U$. $\:$ I think one would also need to show that being an open map to a set that includes $\mathbf{0}$ is an open property, although I imagine that would follow from some result in degree theory. $\hspace{.37 in}$
Sep
29
comment Does the implicit function theorem hold for discontinuously differentiable functions?
@FrancescoPolizzi : $\;\;\;$ Which part of that? $\:$ (Remember that I'm asking about the implicit function theorem, not the inverse function theorem.) $\;\;\;\;\;\;\;$
Sep
29
comment Does the implicit function theorem hold for discontinuously differentiable functions?
@JoonasIlmavirta : $\:$ What I want is something which does show that, $\hspace{2.09 in}$ rather than just can be used to show that. $\;\;\;$
Sep
29
comment Does the implicit function theorem hold for discontinuously differentiable functions?
If one removed the two instances of "continuously" from the text between "Writing all the hypotheses together gives the following statement." and "Regularity", would the resulting statement still be true? $\hspace{.37 in}$
Sep
29
comment What is the most useful non-existing object of your field?
There are (at least) two quite different reasons why such "objects" might be useful: their existence could frequently be the right-hand-side of an implication, or there could be nets/filters of existing objects that "converge" to the non-existent object. $\;$
Sep
29
asked Does the implicit function theorem hold for discontinuously differentiable functions?
Sep
27
awarded  Notable Question
Sep
2
awarded  Popular Question
Jul
31
revised Does the Fourier transform of a non-strictly positive real kernel $\Phi(t)$ always generate entire function with complex zeros?
changed spacing and fixed spelling and grammar