Paving

A set of subsets of a set (or space) containing the empty subset. The elements of the paving are called stones. A set $ \Omega $ together with a paving $ {\mathcal C} $ forms a paved space $ ( \Omega , {\mathcal C} ) $. A compact paving (a compact paved space) is a paving $ {\mathcal C} $( a paved space $ ( \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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