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The structure of equicontinuous maps |
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| Authors: | Jie-Hua Mai |
| Institution: | Institute of Mathematics, Shantou University, Shantou, Guangdong, 515063, People's Republic of China |
| Abstract: | Let  be a metric space, and  be a continuous map. In this paper we prove that if  is compact, and  for all  , then  is equicontinuous if and only if there exist a pointwise recurrent isometric homeomorphism  and a non-expanding map  that is pointwise convergent to a fixed point  such that  is uniformly conjugate to a subsystem  of the product map  . In addition, we give some still simpler necessary and sufficient conditions of equicontinuous graph maps. |
| Keywords: | Metric space equicontinuous map recurrent point uniform conjugacy graph map |
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