ALGEBRALGEBRAIC AND TOPOLOGICAL ANALYSIS OF ENVELOPING SEMIGROUPS IN TRANSFORMATION GROUPS:PROXIMAL EQUIVALENCE AND HOMOMORPHIC IMAGE
Abstract
This paper investigates the algebraic properties of the enveloping semigroupE of a transformation group (X,T,?) with a compact Hausdorff phase space X. The transition group G is considered as a group of homeomorphisms on X, and E is defined as the closureof G in X×X. The main focus is on establishing a connection between the proximal equivalence relation in X and the structure of E, particularly the presence of a unique minimal right ideal. In the latter part, the study extends to the analysis of homomorphic images of transformation groups through their enveloping semigroups.
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