Eduard Heine is best remembered for the Heine-Borel theorem and was responsible for the introduction of the idea of uniform continuity. He was born in Berlin on 16 March 1821 and died in Halle on 21 October 1881. The statement that every open cover of a closed bounded interval has a finite subcover carries his name together with that of Émile Borel, and his insistence on uniform continuity cleared a path through the foundations of nineteenth-century analysis. He was one of the nineteenth-century analysts who made calculus precise.
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Source Eduard Heine, Biography (MacTutor History of Mathematics)
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Source Heine-Borel Theorem (Wikipedia)
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Source Eduard Heine, Biography (MacTutor History of Mathematics)Quick InfoQuote, Quick Info
Born 16 March 1821 Berlin, Germany
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1. Eduard Heine, Biography (MacTutor History of Mathematics)
Quick Info: Born
16 March 1821
Summary
Eduard Heine is best remembered for the Heine-Borel theorem. He was responsible for the introduction of the idea of uniform continuity.
View the SourceHeine-Borel Theorem (Wikipedia)
Wikimedia FoundationPrincipal Result: Heine-Borel Theorem, Lead sentence of the article on the resultQuote, Principal Result: Heine-Borel Theorem, Lead sentence of the article on the result
In real analysis in mathematics, the Heine-Borel theorem, named after Eduard Heine and Émile Borel, states: For a subset S {\displaystyle S} of Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , the following two statements are equivalent: S {\displaystyle S} is compact, that is, every open cover of S {\displaystyle S} has a finite subcover S {\displaystyle S} is closed and bounded.
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