Timeline for Separation property for non-injective flows

7 events

when toggle format	what		by	license	comment
Feb 3, 2020 at 13:29	history	edited	YCor	CC BY-SA 4.0	edited tags, emphasized question
Apr 11, 2018 at 18:35	answer	added	Lénaïc Chizat		timeline score: 1
Apr 10, 2018 at 22:38	history	edited	Lénaïc Chizat	CC BY-SA 3.0	Changed to domain to $\mathbb{R}^d$ for simplicity and consistency.
Apr 10, 2018 at 21:55	comment	added	Lénaïc Chizat		Oh I was imprecise, I indeed mean the second case, let me update my question. Thank you.
Apr 10, 2018 at 20:45	comment	added	user539887		It is not clear to me what you understand by $\partial A$. Is this the boundary in the topology of $\mathbb{R}^d$, or in the relative topology of $\Omega$? I would rather think the latter: $\Omega$ is our "universe". Take $A = \Omega = (-1, 1) \subset \mathbb{R}$ and $X_t(x) = e^{-t}x$. $\partial(X_1(A)) = \{ -e^{-1}, e^{-1} \}$, whereas $X_1(\partial A) = \emptyset$. And if you understand by $\partial A$ its boundary in the topology of the ambient space $\mathbb{R}^d$, the semiflow should be defined on the closure of $\Omega$.
Apr 10, 2018 at 19:39	review	First posts
Apr 10, 2018 at 19:42
Apr 10, 2018 at 19:35	history	asked	Lénaïc Chizat	CC BY-SA 3.0