Completeness and Cocompleteness of R
Smod1 N |
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Authors: | Helmut Röhrl |
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Institution: | (1) 9322 La Jolla Farms Road, La Jolla, CA 92037, USA |
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Abstract: | In this paper we formalize the concept of absolutely convergent infinite series by introducing the notion of prenormed R-semimodule with N-summation, where N is an arbitrary class. The morphisms between such semimodules are the contractive homomorphisms of R-semimodules that `preserve" N-summation. The category
R
Smod
1 N
of all prenormed R-semimodules with N-summation and their morphisms (composition being the set-theoretical one) fails to be an algebraic category. However, under quite general conditions it is both complete and cocomplete. |
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Keywords: | prenormed semimodule N-summation complete cocomplete free objects |
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