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Sur un théorème équivalent à l'hypothèse du continu. (Q1467504)

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scientific article; zbMATH DE number 2608695
Language Label Description Also known as
English
Sur un théorème équivalent à l'hypothèse du continu.
scientific article; zbMATH DE number 2608695

    Statements

    title
    Sur un théorème équivalent à l'hypothèse du continu. (English)
    0 references
    publication date
    1919
    0 references
    review text
    Die Cantorsche Hypothese über die Mächtigkeit des Kontinuums \((2^{\aleph_0} =\aleph_1)\) bildet immer noch das große Rätsel der Mengenlehre. Es wird nun der folgende Satz bewiesen: ``Die Kontinuumhypothese ist äquivalent mit der Existenz einer ebenen Menge \(E,\) die auf jeder Parallelen zur Abszissenachse höchstens abzählbar ist, während die Komplementärmenge \(\bar E\) ihrerseits auf jeder Parallelen zur Ordinatenachse höchstens abzählbar ist.''
    0 references

    Identifiers

    zbMATH DE Number
    2608695
    0 references
     
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