Omega as Limit Point of Intervals of Uncountable Closed Ordinal Space

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Theorem

Let $\Omega$ denote the first uncountable ordinal.

Let $\closedint 0 \Omega$ denote the closed ordinal space on $\Omega$.


Then $\Omega$ is a limit point of the set $\openint a \Omega$, but not the limit point of any sequence of points in $\openint a \Omega$.


Proof



Sources