Abstract

Let G denote an infinite locally compact topological group. In this paper a topological transformation group is constructed in which all topological transformation groups( G, X, π) can be embedded for which X is a completely regular space of weight w( X) ⩽ the Lindelöf degree L( G) of G. As an application, results of de Groot and of de Groot and McDowell are generalized concerning the extension of the action of a group to a completion, resp. a compactification, of the phase space.

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