The contiguity in R/M
The Contiguity in R/M

Anr.e. degree c is contiguous if degwtt(A)=degwtt(B) for anyr.e. setsA, B∈c. In this paper, we generalize the notation of contiguity to the structure R/M, the upper semilattice of ther.e. degree set R modulo the cappabler.e. degree set M. An element c]∈R/M is contiguous if degwtt(A)]=degwtt(B)] for anyr.e. setsA, B such that degT(A) degT(B)∈c]. It is proved in this paper that every nonzero element in R/M is not contiguons, i.e., for every element c]∈R/M, if c]≠o] then there exist at least twor.e. setsA, B such that degT(A), degT(B)∈c] and degwtt(A)]≠degwtt(B)]. The project is partially supported by the National Natural Science Foundation of China under Grant No.19971090.