If $X$ is a reflexive Banach space and $(C_n), n \in \mathbb{N}$ is a sequence of closed convex bounded sets with $C_{n+1}$ contained in $C_n$ for all $n \in \mathbb{N}$. How does one show that the countable intersection of $C_n$ for $n \in \mathbb{N}$ is not the empty set?
countable intersection of closed convex bounded subsets reflexive banach space is non empty.
0
$\begingroup$
banach-spaces
-
0How does one mark some answers as correct? – 2012-06-10
-
0http://meta.stackexchange.com/questions/5234/how-does-accepting-an-answer-work – 2012-06-10