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Topological semigroups and universal spaces related to extension dimension

A. Chigogidze·A. Karasev·M. Zarichnyi
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Abstract

It is proved that there is no structure of left (right) cancelative semigroup on $[L]$-dimensional universal space for the class of separable compact spaces of extensional dimension $\le [L]$. Besides, we note that the homeomorphism group of $[L]$-dimensional space whose nonempty open sets are universal for the class of separable compact spaces of extensional dimension $\le [L]$ is totally disconnected.

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A. Chigogidze, A. Karasev, M. Zarichnyi. 2001-09-17. Topological semigroups and universal spaces related to extension dimension. https://arxiv.org/abs/math/0109106

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