A decomposition theorem for χ1-convex sets

A Convex Decomposition Theorem for 4-Manifolds

An exact manifold with pseudoconvex boundary (PC manifold, for short) is a compact complex manifold X, which admits a strictly pluri-subharmonic Morse function ψ, such that the set of maximum points of ψ coincides with the boundary ∂X. We prefer the term PC manifold, since the combination of words “compact Stein manifold” is likely to precipitate heart palpitations in some mathematicians. Such ...

A Convex Decomposition Theorem for Four - Manifolds

In this article we show that every smooth closed oriented fourmanifold admits a decomposition into two submanifolds along common boundary. Each of these submanifolds is a complex manifold with pseudo-convex boundary. This imply, in particular, that every smooth closed simply-connected four-manifold is a Stein domain in the the complement of a certain contractible 2-complex.

A Representation Theorem for Bounded Convex Sets

An embedding theorem for convex fuzzy sets

In this paper we embed the space of upper semicontinuous convex fuzzy sets on a Banach space into a space of continuous functions on a compact space. The following structures are preserved by the embedding: convex cone, metric, sup-semilattice. The indicator function of the unit ball is mapped to the constant function 1. Two applications are presented: strong laws of large numbers for fuzzy ran...

A fractional Helly theorem for convex lattice sets

A set of the form C-Z ; where CDR is convex and Z denotes the integer lattice, is called a convex lattice set. It is known that the Helly number of d-dimensional convex lattice sets is 2 : We prove that the fractional Helly number is only d þ 1: For every d and every aAð0; 1 there exists b40 such that whenever F1;y;Fn are convex lattice sets in Z such that T iAI Fia| for at least að n dþ1Þ inde...