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Equicontinuity of a graph map

  • Taixiang Sun (a1), Yongping Zhang (a1) and Xiaoyan Zhang (a1)

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Let G be a graph, and f: GG be a continuous map with periodic points. In this paper we show that the following five statements are equivalent.

(1) f is equicontinuous.

(2) There exists some positive integer N such that fN is uniformly convergent.

(3) f is S-equicontinuous for some positive integer sequence S = {n1 < n2 < …}.

(4) Ω(x, f) = ω(x, f) for every xG.

(5) is a periodic map.

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References

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