Results in Mathematics

, Volume 36, Issue 3–4, pp 260–270 | Cite as

Injective Hulls in POSV

  • Ulrich Heckmanns
Research article


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.

Math. Subject Classification

06A23 06A12 18B35 

key words

injective object injective hull V-monotone map semilattice POSV Brouwerian lattice 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G. Bruns and H. Lakser, Injective hulls of semilattices, Canad. Math. Bull. 13 (1970), 115–118.MathSciNetCrossRefMATHGoogle Scholar
  2. [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. [3]
    O. Frink, Ideals in partially ordered sets, Amer. Math. Monthly 61 (1954), 223–234.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    U. Heckmanns, Aspects of ultrametric spaces, Thesis, München 1995.Google Scholar
  5. [5]
    A. Horn and N. Kimura, The category of semilattices, Algebra universalis 1 (1971), 26–38.MathSciNetCrossRefMATHGoogle Scholar
  6. [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).Google Scholar
  7. [7]
    J. Ohm, Semi-valuations and groups of divisibility, Canad. J. Math. 21 (1969), 576–591.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  1. 1.Ulrich Heckmanns, Mathematisches Institut der Universität MünchenMünchen

Personalised recommendations