Ukrainian Mathematical Journal

, Volume 42, Issue 2, pp 161–165 | Cite as

Strong hypercomplex convexity

  • G. A. Mkrtchyan


The concept of a hypercomplex convex set is introduced. The properties of strongly hypercomplex convex sets are considered. A theorem is presented on strong hypercomplex convexity. A hypercomplex version of the geometric form of the Hahn-Banach Theorem is established.


Geometric Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    V. A. Rokhlin and D. B. Fuks, Initial Topology Course. Geometric Chapters [in Russian], Nauka, Moscow (1977).Google Scholar
  2. 2.
    L. A. Aizenberg, A. P. Yuzhakov, and L. Ya. Makarova, “Linear convexity in ℂπ,” Sib. Mat. Zh.,9, No. 4, 773–746 (1968).Google Scholar
  3. 3.
    E. H. Spanier, Algebraic Topology, Springer, New York (1966).Google Scholar
  4. 4.
    Yu. B. Zelinskii, “A strong convexity criterion,” in: The Geometric Theory of Functions and Topologies [in Russian], pp. 18–29, Mathematics Institute, Academy of Sciences of the Ukrainian SSR, Kiev (1981).Google Scholar
  5. 5.
    G. A. Mkrtchyan, “Hypercomplex convex sets,” Preprint No. 87.42, Mathematics Institute, Academy of Sciences of the Ukrainian SSR (1987).Google Scholar
  6. 6.
    N. Bourbaki, Espaces Vectoriels Topologiques, Hermann, Paris (1953).Google Scholar
  7. 7.
    Yu. B. Zelinskii, “The Hahn-Banach Theorem for strongly linear convex domains,” Reports of the extended sessions of a seminar of the I. N. Vekua Institute of Applied Mathematics, Vol. 1, No. 1, 79–81, Tbilisi State University (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • G. A. Mkrtchyan
    • 1
  1. 1.Yerevan National Economic InstituteUSSR

Personalised recommendations