In most books on mathematics, when discussing the space $L^2(\Omega)$ of square-integrable functions defined on $\Omega\subset\mathbb{R}^N$, it is often assumed that $\Omega$ is a connected open set. Do any technical problems arise if assume $\Omega$ to be a closed set?
2026-04-06 12:22:20.1775478140
$L^2(\Omega)$ Hilbert space
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