# Open Real Interval is not Compact

## Theorem

Let $\R$ be the real number line considered as an Euclidean space.

Let $I = \left({a \,.\,.\, b}\right)$ be an open real interval.

Then $I$ is not compact.

## Proof

From Open Real Interval is not Closed Set, $I$ is not a closed set of $\R$.

The result follows by definition of compact.

$\blacksquare$