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Injective Hulls in POSV

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Abstract

We determine the injective objects and hulls in the category POSV. This category is similar to the one of join semilattices but contains all partially ordered sets. The results of this paper have applications, for instance, in the theory of (generalized) ultrametric spaces.

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References

  1. G. Bruns and H. Lakser, Injective hulls of semilattices, Canad. Math. Bull. 13 (1970), 115–118.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Erné, Adjunctions and standard constructions for partially ordered sets, in: Contributions to general algebra, 2 (Klagenfurt, 1982), 77–106, Holder-Pichler-Tempsky, Vienna, 1983.

    Google Scholar 

  3. O. Frink, Ideals in partially ordered sets, Amer. Math. Monthly 61 (1954), 223–234.

    Article  MathSciNet  MATH  Google Scholar 

  4. U. Heckmanns, Aspects of ultrametric spaces, Thesis, München 1995.

  5. A. Horn and N. Kimura, The category of semilattices, Algebra universalis 1 (1971), 26–38.

    Article  MathSciNet  MATH  Google Scholar 

  6. E. M. Jawhari, D. Misane and M. Pouzet, Retracts: graphs and ordered sets from the metric point of view, in: Combinatorics and ordered sets (Arcata, Calif., 1985), 175-226, Contemp. Math., 57 (1986).

  7. J. Ohm, Semi-valuations and groups of divisibility, Canad. J. Math. 21 (1969), 576–591.

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Ulrich Heckmanns.

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Heckmanns, U. Injective Hulls in POSV . Results. Math. 36, 260–270 (1999). https://doi.org/10.1007/BF03322115

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  • DOI: https://doi.org/10.1007/BF03322115

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