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Article | REF: AF120 V1

Metric Spaces I. Basic Notions

Author: Jean-Charles PINOLI

Publication date: July 10, 2018

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8. Notions of connectedness

8.1 Connections

In a metric space, a ball is not necessarily connected by paths (p. 225 of ).

Theorem of Mazurkiewicz (1913, 1916), Moore (1916) and Menger (1929). A complete, locally connected metric space is locally connected by paths (p. 254 of ).

Theorem of Hahn (1914) and Mazurkiewicz (1920). A separate nonempty topological space T ...

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