Topological semigroups and universal spaces related to extension dimension

Details Topological semigroups and universal spaces related to extension dimension Topological semigroups and universal spaces related to extension dimension

2001-09-17

arxiv.org/abs/math/0109106v1

Mathematics

General Topology

Scientific paper

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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