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 ⇄Suchrichtung
 Übersetzung für 'Heine-Borel' von Englisch nach Deutsch
math.
Heine-Borel theorem [also: theorem of Heine-Borel, theorem of Heine and Borel]
Satz {m} von Heine-Borel
math.
Heine-Borel theorem [also: theorem of Heine-Borel, theorem of Heine and Borel]
Überdeckungs­satz {m} (von Heine-Borel) [auch: Heine-Borel'scher Überdeckungs­satz]
2 Übersetzungen
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  • Satz {m} von Heine-Borel = Heine-Borel theorem [also: theorem of Heine-Borel, theorem of Heine and Borel]
  • Überdeckungssatz {m} (von Heine-Borel) [auch: Heine-Borel'scher Überdeckungssatz] = Heine-Borel theorem [also: theorem of Heine-Borel, theorem of Heine and Borel]
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Anwendungsbeispiele Englisch
  • Note that these measures of non-compactness are useless for subsets of Euclidean space R"n": by the HeineBorel theorem, every bounded closed set is compact there, which means that γ("X") = 0 or ∞ according to whether "X" is bounded or not.
  • In particular, no infinite–dimensional normed space can be locally compact or have the HeineBorel property.
  • The equivalence of the definition with the definition of compactness based on subcovers, given later in this section, is known as the Heine-Borel theorem.
  • This is analogous to the HeineBorel theorem, which states that subsets of R"n" are compact if and only if they are closed and bounded.
  • Every closed interval in R of finite length is compact. More is true: In R [...] , a set is compact if and only if it is closed and bounded. (See HeineBorel theorem).

  • This form of the theorem makes especially clear the analogy to the HeineBorel theorem, which asserts that a subset of [...] is compact if and only if it is closed and bounded.
  • This space is closed and bounded and so compact by the HeineBorel theorem, but has similar properties to the topologist's sine curve—it too is connected but neither locally connected nor path-connected.
  • This is a generalization of the HeineBorel theorem, which states that any closed and bounded subspace [...] of [...] is compact and therefore complete.
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