In pattern analysis and image management, 

the information of an objectiveimage can be recovered 

from a sequence approximate images. In mathematical form of 

expression we need to consider some types of continuity. 

In [3], W.Gong defined the upper limit and lower limit of 

a sequence, and the concepts are used to characterize 

the convergency and continuity in the space consisting of 

images. In the present paper, we shall give first 

some examples to show that there are some theoretical 

shortcomings in [3], and furthermore we shall prove

some corresponding correct results.