Paving

A set of subsets of a set (or space) containing the empty subset. The elements of the paving are called stones. A set $\mathrm{\Omega }$ together with a paving $\mathcal{C}$ forms a paved space $(\mathrm{\Omega },\mathcal{C})$. A compact paving (a compact paved space) is a paving $\mathcal{C}$( a paved space $(\mathrm{\Omega },\mathcal{C})$) with the finite intersection property: for every finite subset $\{C_1\dots C_n\}\subset \mathcal{C}$, ${\cap }_{i=}{1}^n{C}_i$ is non-empty.

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