Abstract:
Topological groups of transformations are studied (their structure and equivariant compactifications) on which the pointwise convergence topology is an admissible group topology. It is proved that the pointwise convergence topology is an admissible group topology and coincides with the topology of uniform convergence on the group of order-preserving homeomorphisms of a linearly ordered compactum. These groups are described for some lexicographically ordered products. The groups of homeomorphisms of a closed interval, of the “Double Arrow” Alexandroff space, of the lexicographically ordered square, and of the closed extended long ray are regarded as examples of the use of the general statements thus obtained.
Keywords:admissible group topology, totally bounded uniformity, Roelcke precompactness, equivariant compactification.
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