The Roelcke Precompactness and Compactifications of Transformations Groups of Discrete Spaces and Homogeneous Chains

TL;DR

This paper investigates the Roelcke precompactness of transformation groups acting on discrete spaces and chains, constructing compactifications via the Ellis method for ultratransitive actions.

Contribution

It introduces new insights into the Roelcke precompactness of transformation groups and develops compactifications for ultratransitive actions using the Ellis construction.

Findings

Characterization of Roelcke precompactness in specific transformation groups

Construction of compactifications for ultratransitive actions

Application of Ellis construction to permutation and LOTS topologies

Abstract

The Roelcke precompactness of transformation groups of discrete spaces and chains in the permutation topology and LOTS in the topology of pointwise convergence is studied. For ultratransitive actions compactifications of transformation groups using the Ellis construction are built.