Point-finite collection explained

l{U} of subsets of a topological space X is said to be point-finite if every point of X lies in only finitely many members of l{U}. ^[1]

A metacompact space is a topological space in which every open cover admits a point-finite open refinement. Every locally finite collection of subsets of a topological space is also point-finite. A topological space in which every open cover admits a locally finite open refinement is called a paracompact space. Every paracompact space is therefore metacompact.^[1]

Notes and References

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