- #1

cragar

- 2,552

- 3

## Homework Statement

Give an example of an infinite collection of nested open sets.

[itex] o_1 \supseteq o_2 \supseteq o_3 \supseteq o_4 ... [/itex]

Whose intersection [itex] \bigcap_{n=1}^{ \infty} O_n [/itex] is

closed and non empty.

## Homework Equations

A set [itex] O \subseteq \mathbb{R} [/itex] is open if for all points, [itex] a \in O [/itex]

there exists an [itex] \epsilon [/itex] neighborhood [itex] V_{\epsilon}(a) \subseteq O [/itex]

## The Attempt at a Solution

It seems like if we started with the open interval (0,1) and then took a smaller interval that was nested inside the original interval, and then just kept doing this until we enclosed one point in the interval.