MAT322(Metric Space)

**ajibolaadebisi** · May 22nd 2012, 07:26 AM

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

**Plato** · May 22nd 2012, 08:13 AM

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?

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