2013/11/04 by Walter Briec, Briec, Walter
Computer Science · Decision Sciences · Engineering · #Optimization and Variational Analysis #Fuzzy and Soft Set Theory #Control and Dynamics of Mobile Robots
paper · pdf · doi:10.48550/arxiv.1311.0690
\mathbb B-convexity was defined in [7] as a suitable Kuratowski-Painlevé upper limit of linear convexities over a finite dimensional Euclidean vector space. Excepted in the special case where convex sets are subsets of \mathbb Rn_ +, \mathbb B-convexity was not defined with respect to a given explicit algebraic structure. This is done in that paper, which proposes an extension of \mathbb B-convexity to the whole Euclidean vector space. An unital idempotent and non-associative magma is defined over the real set and an extended n-ary operation is introduced. Along this line, the existence of the Kuratowski-Painlevé limit of the convex hull of two points over \mathbb Rn is shown and an explicit extension of \mathbb B-convexity is proposed.