Abstract
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)].
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The project is partially supported by the National Natural Science Foundation of China under Grant No.19971090.
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Zhang, Z., Yuefei, S. The contiguity in R/M. J. Comput. Sci. & Technol. 17, 507–511 (2002). https://doi.org/10.1007/BF02943291
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DOI: https://doi.org/10.1007/BF02943291