For a finite tree and its endpoint ⊥, a natural partial order ≤ is defined such that ⊥ is the greatest element in T.Continuous function f is a kind of generalized fuzzy function. Moreover, let ↓f（x,t):t≤f(x)} and ↓C(X,T)={↓f:f is continous from X to T}. The subspace ↓C(X,T) is the family of all non-empty closed sets in X×T with the Hausdorff distance. Let Si is a segment of T,↓CUB(Si)={↓f∈↓(X×T):max f(X)∈Si\\{vi}}.For any SiT, the closure of ↓CUB(Si) is given.