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On $\mathbb R$-embeddability of almost disjoint families and Akemann–Doner C$^*$-algebras
An almost disjoint family $\mathcal A$ of subsets of $\mathbb N$ is said to be $\mathbb R$-embeddable if there is a function $f:\mathbb N\rightarrow \mathbb R$ such that the sets $f[A]$ are ranges of real sequences converging to distinct reals for di