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  "body": "\n## Summary\n\nA metacompact space is a [[topological space|0CQHFPGJ45]] in which every [[open cover|049PXYHW1T]] has a point-finite open refinement.\nPoint-finite means that each point lies in only finitely many members of the refinement.\nThis is weaker than [[paracompactness|8R29G6NG9Q]], where each point needs a neighbourhood meeting only finitely many members.\nSo every paracompact space, and in particular every compact space, is metacompact.\n\n## Explanations\n\n### L1 human\n\nIn a metacompact space, you can always shrink an open cover so that no point is covered too many times.\nEach single point sits in only finitely many of the new sets.\nPoints close to it may still be covered by many different sets.\nThat is the difference from paracompact spaces, where a whole neighbourhood must see only finitely many sets.\n",
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