290 reputation
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bio website topologia-geral.ourproject.or…
location Brasília - Brasil
age 36
visits member for 2 years, 10 months
seen 20 hours ago

PhD student at UnB.

Fond of free software and freedom of knowledge. :-)

You can contact me at:
andre.em.caldas@gmail.com


Aug
10
awarded  Nice Question
Mar
28
awarded  Popular Question
Nov
18
awarded  Nice Question
Sep
30
awarded  Yearling
Apr
4
awarded  Necromancer
Jan
3
comment Supremum amongst Kolmogorov-Sinai entropies: ergodic or just invariant measures.
How do you prove that $\mu(X) = 1$ implies $m(X) = 1$ for $\tau$-a.e. $m$? Remember that having an "ergodic decomposition" means that for every continuous $\phi: \widetilde{X} \to \mathbb{R}$, $\int \phi d\mu = \int_{E(T)} \int \phi dm d\tau$. Also, notice that it might happen that $X \neq T^{-1}X$.
Oct
13
revised locally connected versus locally compact
Fixed math statement.
Oct
13
comment locally connected versus locally compact
This is a very neat way to justify my intuitive but not so elaborate and well justified belief that any neighborhood should have the property. Note taken! :-) I think of a neighborhood as a "sufficiently large set". Large enough to be considered a neighborhood. Often, one needs to choose a "small" set, but at the same time, big enough to make the small step big enough to achieve the goal... "path connect two points", for instance.
Oct
13
comment Infinite dimensional vector spaces with compact unit ball
I liked your question, Leandro! I had never thought of $\mathbb{R}$ as a infinite dimensional space with compact unit ball! You opened my mind a bit! :-) +1
Oct
13
comment locally connected versus locally compact
Which one is your "standard 'locally <blank>' definition"? :-)
Oct
13
answered locally connected versus locally compact
Oct
11
comment Extending open maps to Stone-Cech compactifications
The extension is unique, are you just asking if the extension is or not an open surjection?
Oct
9
accepted Compact group extension of a zero entropy system.
Oct
7
comment Compact group extension of a zero entropy system.
@Asaf: Thank you very much for the help. I will study your answer. :-)
Oct
5
comment Compact group extension of a zero entropy system.
By the way, a similar argument to "Lemma 7" is used in Theorem 2.3 of "On Li-Yorke Pairs": imath.kiev.ua/~skolyada/LY.pdf "Since an isometric extension of a zero-entropy system has still entropy zero [...]"
Oct
5
comment Compact group extension of a zero entropy system.
@Asaf: Oops... (again!) Sorry for not paying the attention you deserve! Theorem 8.2 reads: If $(X, \mathcal{B}, \mu, T)$ is an ergodic isometric extension of $(Y, \mathcal{D}, \nu, T)$ then $(X, \mathcal{B}, \mu, T)$ is a factor of an ergodic group extension of $(Y, \mathcal{D}, \nu, T)$. In Furstenberg's paper, the definition for isometric extensions is quite complicated, but there is a comment (p. 236) saying: Extensions for which $\mathcal{E}(X|Y,T) = L^2(X)$ will be called isometric extensions.
Oct
5
revised Compact group extension of a zero entropy system.
Changed the measure to be ergodic.
Oct
5
comment Compact group extension of a zero entropy system.
@Asaf: I will have to study a bit more to fully understand your comments... :-) I guess I am forgetting the fact that $\mu$ is supposed to be ergodic. I will edit (again!) the post. By the way, I am trying to make sense of the demonstration of Lemma 7 at math.u-psud.fr/~ruette/articles/asympent.pdf
Oct
5
revised Compact group extension of a zero entropy system.
Fixed: Elements of K are supposed to be measure-preserving.
Oct
5
comment Compact group extension of a zero entropy system.
@Asaf: Oops... you are right. It is a very good example. I will fix the post.