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.
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- 1.V. A. Rokhlin and D. B. Fuks, Initial Topology Course. Geometric Chapters [in Russian], Nauka, Moscow (1977).Google Scholar
- 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.E. H. Spanier, Algebraic Topology, Springer, New York (1966).Google Scholar
- 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.G. A. Mkrtchyan, “Hypercomplex convex sets,” Preprint No. 87.42, Mathematics Institute, Academy of Sciences of the Ukrainian SSR (1987).Google Scholar
- 6.N. Bourbaki, Espaces Vectoriels Topologiques, Hermann, Paris (1953).Google Scholar
- 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