【摘要】 证明 8字空间上连续映射 f:8→ 8是等度连续的充分必要条件是下列条件之一成立 :( 1 ) {fj·4!}∞j=1 是一致收敛的 ;( 2 )存在一个正整数k ,使得 {fj·k}∞j=1 是一致收敛的。更多还原

【Abstract】 Let 8 be the figure-eight space and f∶8→8 be the continuous map with a periodic point. In this paper we show that f is equicontinuous if and only if one of the following holds: (1) {f j·4! } ∞ j=1  is uniformly convergent. (2) There exists a positive integer k, such that {f j·k } ∞ j=1  is uniformly convergent.更多还原