Refinement

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Definition

Let U_i, i \in I be a cover of a topological space X, viz a collection of subsets of X whose union is X. A refinement of U_i is another cover V_j, j \in J such that for any j, there exists an i such that V_j \subseteq U_i.

An open refinement is a refinement where the new cover is an open cover.

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