ハイネ・ボレルの被覆定理




ハイネ・ボレルの被覆定理（ハイネ・ボレルのひふくていり）とは、数学の定理で、次のような定理である。



ユークリッド空間 Rn の部分集合 S について、次の二つは同値


  1. S は、有界閉集合


  2. S は、コンパクト



また、次のように一般化される。



距離空間において、部分集合がコンパクトであることと、完備全有界であることは同値。


関連項目



  • エドゥアルト・ハイネ

  • エミール・ボレル




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