Abstract
If G is a locally compact topological group, let BC(G) denote the set of real-valued, bounded, uniformly continuous functions on G with the compact-open topology. Using the fact that the distal (weakly distal) functions are the elements of BC(G) whose orbit closures are compact distal (point-distal) minimal sets, we can characterize compact distal and point-distal minimal transformation groups. Let (X, G, A) be a right transformation group where X is compact Hausdorff and minimal under G. Then X is a compact distal (point-distal) minimal set if and only if there is a point xCX such that for any homomorphism h: X-*BC(G), h(x) is a right distal (weakly distal) function.
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