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TOPOLOGICAL TRANSFORMATION GROUPS
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ation group automorphic Banach space canonical projection Cartesian product closed invariant equivalence cocycle commutative diagram compact minimal set compact phase space compact solution compact space compact subset continuous map Corollary Define a map dense distal extension distal minimal dynamical system easy to verify equicontinuous extension exists a point exists an element fibre finite follows from Lemma formation group function group and let group extension group G homomorphism idempotent identity implies induces invariant equivalence relation isomorphism Let us prove Let X,T limit ordinal locally almost periodic metric space metrizable minimal cascade minimal extension minimal right ideal minimal transformation group non-empty periodic point point x e point xeX Proof proximal quotient space satisfying the condition semigroup space and let subgroup of G subsemigroup Suppose tion topological space topological transformation group transformation group X,T uniform space uniformly synchronous