MAT322(Metric Space)

• May 22nd 2012, 08:26 AM
MAT322(Metric Space)
If A1,A2,......An, is a collection of n number of sets in a metric space, prove that their intersection is open.
• May 22nd 2012, 09:13 AM
Plato
Re: MAT322(Metric Space)
Quote:

Originally Posted by ajibolaadebisi
If A1,A2,......An, is a collection of n number of sets in a metric space, prove that their intersection is open.

As written that statement is false.
If each of the $A_i$ is closed and $\bigcap\limits_n {{A_n}} \ne \emptyset$ then $\bigcap\limits_n {{A_n}}$ is closed.

Did you mean each of the $A_i$ is open?