Morphisms of Stonian Cones

  • Eugen Popa


The main result of this paper puts forward a class of morphisms of H-cones, possessing image: namely those commuting with arbitrary infimum. Applying this result to the canonical embedding in the bidual, one gets a decomposition of any H-cone In the particular case when the cone has the specific order, this decomposition gives a well-known theorem of Dixmier [1], on the structure of stonian compact spaces.


Compact Space Normal Measure Specific Order Injective Morphism Canonical Morphism 
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  1. [1]
    J. Dixmier, Sur certains espaces considérés par M.H. Stone, Summa Bras. Math. 151, 1951.Google Scholar
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    N. Boboc, Gh. Bucur, A. Cornea, Order and Convexity in Potential Theory: H-cones, Lecture Notes in Mathematics, vol. 853, Springer-Verlag, 1981.Google Scholar
  3. [3]
    N. Boboc, Gh. Bucur, Stonian Structures in Potential Theory, Preprint INCREST, Bucureşti, 52/1984.Google Scholar
  4. [4]
    E. Popa, Morphisms of H-cones, An. Şt. Univ. Iasi, t. XXIX, f. 2 (1983).Google Scholar
  5. [5]
    E. Popa, Morphisms of H-cones and Semi-polar Sets, An. Şt. Univ. Iaşi, t. XXX, f. 3 (1984).Google Scholar
  6. [6]
    E. Popa, Finely Open Morphisms of H-cones, Math. Ann. 270 (1985).Google Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • Eugen Popa
    • 1
  1. 1.Seminarul MatematicUniversitatea “Al. I. Cuza”IaşiRomania

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