Connected, not separably connected complete metric spaces

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In a separably connected space any two points are contained in a separable connected subset. We show a mechanism that takes a connected bounded metric space and produces a complete connected metric space whose separablewise components form a quotient space isometric to the original space. We repeatedly apply this mechanism to construct, as an inverse limit, a complete connected metric space whose each separable subset is zero-dimensional.
10 pages

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General Topology, Metric Geometry, 54D05; 54C30

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http://salesiana.dossiersoluciones.com/handle/123456789/224950

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0903.4768
 http://arxiv.org/abs/0903.4768

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arXiv