函数列一致连续和一致收敛及等度连续的关系

连续、一致连续、一致收敛和等度连续是函数或函数列非常重要的性质.针对收敛的函数列,探讨了一致连续、一致收敛和等度连续两两之间的关系,并在有界区间上给出了一致连续、一致收敛和等度连续的等价关系.;Continuity,uniform continuity,uniform convergence and equicontinuity are very important qualities of functions or sequence of functions.For sequence of functions,the relation of uniform continuity,uniform convergence and equicontinuity is studied.Their equivalence relation is presented with sequence of functions set in a bounded interval