Abstract:
The (topological) isomorphism of the automorphism group of a homogeneous chain $X$ and the (topological) wreath product of automorphism groups of a regular interval $J$ with respect to the group of automorphisms of the quotient space $X/J$ is established. A characterization of the Roelcke-precompactness of automorphism groups of general chains is given. The equivalence of the Roelcke precompactness of the automorphism group of a general chain in permutation topology and pointwise convergence topology in the presence of a simple proper regular interval is established.
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