4
$\begingroup$

Let $(E,d)$ a metric space. We say that $E$ is a connected space if the only subsets which are both open and closed (clopen sets) are $E$ and the empty set. A subset of $E$ is connected if is a connected subspace of $E$. Let $\{C_i\}_{i\in I}$ a family of connected subsets of $E$. Is $\bigcap_{i\in I} C_i$ a connected subset of $E$?

Thanks for any boost.

  • 0
    Nice! :) :) :) :)2011-08-04

1 Answers 1

8

[Sorry, I should know by now to leave answers as answers, not as comments.]

Once more:

Try intersecting a circle and a line in $\mathbb{R}^2$.