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Erweiterung einer stetigen Abbildung

In: Gesammelte Werke

Author

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  • F. Hausdorff

Abstract

Auszug Der metrische Raum E werde durch ū=f(u) stetig auf den metrischen Kaum Ē abgebildet. Es sei uv die Entfernung zweier Punkte u, v in E und ūv die Entfernung ihrer Bilder ū, v in Ē; bei gegebener Abbildung ist ūv eine gegebene Funktion von u, v mit den Eigenschaften: $$ \begin{array}{l} \left( \alpha \right) \overline {uv} = \overline {vu} \ge 0, \overline {uu} = 0; \\ \left( \beta \right) \overline {uv} + \overline {vw} \ge \overline {uw} ; \\ \left( \gamma \right) \overline {uv} \to 0, falls v \to u \left( {d.h. uv \to 0 bei festem u} \right) \\ \end{array} $$ .

Suggested Citation

  • F. Hausdorff, 2008. "Erweiterung einer stetigen Abbildung," Springer Books, in: Gesammelte Werke, pages 555-568, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-76807-4_16
    DOI: 10.1007/978-3-540-76807-4_16
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