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Separation of Two Sets in a Product Space

✍ Scribed by Reinhard Nehse

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
413 KB
Volume
97
Category
Article
ISSN
0025-584X

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✦ Synopsis

In order to prove fundamental assertions in several fields of mathematics (for instance in functional analysis and in optimization theory) i t is useful to have convenient separation theorems.

The purpose of this paper is to give necessary conditions for convexity of sets in a product space which can be separated by a 'honvertical" affine manifold. Additionally, generalizations of the HAHN-BANACH-Theorem are given.

With this paper we have continued and completed our studies in [5], [6], [8] and [9].

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In [Blokhuis and Lavrauw (Geom. Dedicata 81 (2000), 231-243)] a construction of a class of two-intersection sets with respect to hyperplanes in PGΓ°r Γ€ 1; q t Þ; rt even, is given, with the same parameters as the union of Γ°q t=2 Γ€ 1Þ=Γ°q Γ€ 1Þ disjoint Baer subgeometries if t is even and the union of Γ°