Open Real Interval is not Compact

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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.

$\blacksquare$


Also see


Sources