Connected, not separably connected complete metric spaces

Details Connected, not separably connected complete metric spaces Connected, not separably connected complete metric spaces

2009-03-27

arxiv.org/abs/0903.4768v1

Mathematics

General Topology

10 pages

Scientific paper

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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