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This was previously asked and bountied at math.stackexchange with no response. I've also tweaked the language for clarity; see the edit history for the broader context, and note that the existing ...

Previously asked and bountied at MSE with slightly different language: Given a topological space $\mathcal{X}$, let $$\mathsf{Cl_C}(\mathcal{X})=\bigcup_{n\in\mathbb{N}}C(\mathcal{X}^n,\mathcal{X})$$ ...