Omega as Limit Point of Intervals of Uncountable Closed Ordinal Space

Theorem
Let $\Omega$ denote the first uncountable ordinal.

Let $\left[{0 \,.\,.\, \Omega}\right]$ denote the closed ordinal space on $\Omega$.

Then $\Omega$ is a limit point of the set $\left({a \,.\,.\, \Omega}\right)$, but not the limit point of any sequence of points in $\left({a \,.\,.\, \Omega}\right)$.