A Characterization of the Almost Periodic Homeomorphisms on the Closed 2-cell
نویسنده
چکیده
2. A topological classification of the almost periodic homeomorphisms on a closed 2-cell. A homeomorphism A of a metric space (X, p) onto itself is said to be almost periodic on X if €>0 implies that there exists a relatively dense sequence {«¿} of integers such that p(x, A"*'(x)) <e for all xGA and i= ±1, ±2, • • •. A homeomorphism A of the space X onto itself is said to be topologically equivalent to a homeomorphism / of the space Y onto itself if there exists a homeomorphism ß of X onto Y such that A = ß_1/ß. If A and / are topologically equivalent, it is clear that A is almost periodic on X if and only if / is almost periodic on Y. By a closed 2-cell we mean any homeomorphic image of the unit disk. With these definitions it suffices to consider almost periodic homeomorphisms on the unit disk D. Denote the metric in D by d(-, ■). Kerékjártó's result [5, p. 224] for periodic homeomorphisms may be stated as follows:
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