On the limit problem of compound function

Compound function
Three sets
Two mappings
aggregate 1 ------- mapping 1->-------- aggregate 1 Image of ∈ aggregate 2
aggregate 1 Image of ------------- mapping 2->---------- aggregate 1 The image of ∈ aggregate 3

Fear is fear aggregate 1 The image becomes a collection 2 A point on ！！！！1
We should have changed continuously together , As a result, some people were lazy ,
This limit process can't go on
The limit process cannot be carried out , The limits of composite functions no longer exist