Abstract
phism h of the space X onto itself is said to be topologically equivalent to a homeomorphism f of the space Y onto itself if there exists a homeomorphism a of X onto Y such that h =t3-lf3. If h and f are topologically equivalent, it is clear that h is almost periodic on X if and only if f 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(., *).
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