Baroni’s theorem

Let ${(x_n)}_{n\ge 0}$ be a sequence of real numbers such that $\underset{n\to \mathrm{\infty }}{lim}(x_{n+1}-x_n)=0$. Let $A=\{x_n|n\in \mathbb{N}\}$ and A’ the set of limit points of $A$. Then A’ is a (possibly degenerate) interval from $\overline{ℝ}$, where $\overline{ℝ}=ℝ\bigcup \{-\mathrm{\infty },+\mathrm{\infty }\}$

Title	Baroni’s theorem
Canonical name	BaronisTheorem
Date of creation	2013-03-22 13:32:30
Last modified on	2013-03-22 13:32:30
Owner	mathwizard (128)
Last modified by	mathwizard (128)
Numerical id	6
Author	mathwizard (128)
Entry type	Theorem
Classification	msc 40A05