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What is an example of a hypergraph $H=(V,E)$ with $|e|\geq \aleph_0$ for all $e\in E$ and the property that $H\cong H^*$ where $H^*$ is the dual hypergraph of $H$?

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Let $V = \mathbb R$ and $E = \{(-\infty,r] : r \in \mathbb R\}$.

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