In pattern analysis and image management, the information of 
an objective image can be recovered from a sequence approximate 
images. In mathematical form of expression we need to consider 
some types of continuity. Many researchers defined the limit 
and the upper limit  of a sequence, using the concepts, 
characterized continuity in the space consisting of images. 
In the present paper, we shall give firstly some examples to 
show that there are some theoretical shortcomings in those 
results, then  we shall give some corresponding correct results.