Complete Erdős Space Is Unstable
نویسندگان
چکیده
It is proved that the countably infinite power of complete Erdős space Ec is not homeomorphic to Ec. The method by which this result is obtained consists of showing that Ec does not contain arbitrarily small closed subsets that are one-dimensional at every point. This observation also produces solutions to several problems that were posed by Aarts, Kawamura, Oversteegen, and Tymchatyn. In addition, we show that the original (rational) Erdős space does contain arbitrarily small closed sets that are one-dimensional at every point.
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