Abstract
This paper continues recent work on N-summations (see [8, 9, 12]). More specifically, it addresses the issue of existence of N-summations both for cone semirings and for prenormed semitopological semimodules. In the case of a cone semiring C we assume N-order completeness plus compatibility of N-joins with addition and multiplication to make the class of summarily bounded elements of C N into an N-summation for C. In the case of a prenormed semitopological semimodule M we use certain completeness properties of semitopologies on M to make the class of Cauchy elements of M N into an N-summation for M. Results on semitopologies and their connection with closure operators are contained in the Appendix.
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Fillmore, J., Pumplün, D. & Röhrl, H. On N-Summations, I. Applied Categorical Structures 10, 291–315 (2002). https://doi.org/10.1023/A:1015215528380
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DOI: https://doi.org/10.1023/A:1015215528380