The structure of equicontinuous maps

Author:
Jie-Hua Mai

Journal:
Trans. Amer. Math. Soc. **355** (2003), 4125-4136

MSC (2000):
Primary 54E40, 54H20; Secondary 37B20, 37E25

Published electronically:
June 18, 2003

MathSciNet review:
1990578

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

**Jie-Hua Mai**

Affiliation:
Institute of Mathematics, Shantou University, Shantou, Guangdong, 515063, People’s Republic of China

Email:
jhmai@stu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9947-03-03339-7

Keywords:
Metric space,
equicontinuous map,
recurrent point,
uniform conjugacy,
graph map

Received by editor(s):
March 4, 2002

Received by editor(s) in revised form:
November 1, 2002

Published electronically:
June 18, 2003

Additional Notes:
Project supported by the Special Foundation of National Prior Basic Researches of China (Grant No. G1999075108)

Article copyright:
© Copyright 2003
American Mathematical Society