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The contiguity in R/M

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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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Authors and Affiliations

  1. Department of Computer Science, Yangzhou University, 225009, Jiangsu, P.R. China

    Zhang Zaiyue

  2. Institute of Computing Technology, The Chinese Academy of Sciences, 100080, Beijing, P.R. China

    Sui Yuefei

Authors
  1. Zhang Zaiyue
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  2. Sui Yuefei
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Corresponding author

Correspondence to Zhang Zaiyue.

Additional information

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

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