One Dimensional Locally Connected S-spaces

Details One Dimensional Locally Connected S-spaces One Dimensional Locally Connected S-spaces

2007-10-04

arxiv.org/abs/0710.1085v1

Mathematics

General Topology

13 pages

Scientific paper

We construct, assuming Jensen's principle diamond, a one-dimensional locally connected hereditarily separable continuum without convergent sequences. The construction is an inverse limit in omega_1 steps, and is patterned after the original Fedorchuk construction of a compact S-space. To make it one-dimensional, each space in the inverse limit is a copy of the Menger sponge.

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