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Über die Dimension von Punktmengen III

In: Selecta Mathematica

Author

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  • Karl Menger

Abstract

Zusammenfassung Unter den bisher ungelösten Problemen der Dimensionstheorie ist prinzipiell von besonderer Wichtigkeit die Aufgabe, die Dimension unter den Mengenfunktionen axiomatisch zu charakterisieren, eine Aufgabe, deren Analogon für den Maßbegriff seit langem gelöst ist. Es handelt sich um die Angabe einiger einfacher Forderungen an eine Mengenfunktion, deren Erfülltsein notwendig und hinreichend dafür ist, daß die Funktion mit der Dimension identisch sei. Der vorliegende Aufsatz enthält Untersuchungen über diesen bisher noch ganz unbearbeiteten Fragenkomplex und gibt eine vollständige Lösung des Problems für die Teilmengen der Ebene. Nach eingehender Behandlung der Ebene werden die entsprechenden Verhältnisse in der Geraden, in nulldimensionalen und eindimensionalen Räumen sowie in höherdimensionalen euklidischen Räumen untersucht.

Suggested Citation

  • Karl Menger, 2002. "Über die Dimension von Punktmengen III," Springer Books, in: Bert Schweizer & Abe Sklar & Karl Sigmund & Peter Gruber & Edmund Hlawka & Ludwig Reich & Leopold Sc (ed.), Selecta Mathematica, pages 93-118, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-6110-4_9
    DOI: 10.1007/978-3-7091-6110-4_9
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