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arXiv · 0903.4768

Connected, not separably connected complete metric spaces

T. Banakh·M. Vovk·M. R. Wójcik
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Abstract

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.

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T. Banakh, M. Vovk, M. R. Wójcik. 2009-03-27. Connected, not separably connected complete metric spaces. https://arxiv.org/abs/0903.4768

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