Data di Pubblicazione:
2008
Citazione:
A simple geometric proof of a theorem for starshaped unions of convex sets / L. Vesely. - In: ACTA UNIVERSITATIS CAROLINAE. MATHEMATICA ET PHYSICA. - ISSN 0001-7140. - 49:(2008), pp. 79-82.
Abstract:
Let F be a family of n+1
convex sets in R^d, each n of
which have a point in common, such that F is starshaped.
If either all members of F are closed or all members of
F are open, then the intersection of F is nonempty. This
result which strengthens a theorem by V.Klee
follows from a topological theorem of C.D.Horvath and M.Lassonde. We present a simple geometric proof in the
spirit of Klee''s proof. This immediately provides an alternative proof of a Helly
type theorem due to M.Breen. An abstract vector space variant of the above
result is given, too.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
L. Vesely
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