  $\mathbb B$-convexity was defined in [7] as a suitable Kuratowski-Painlev\'e
upper limit of linear convexities over a finite dimensional Euclidean vector
space. Excepted in the special case where convex sets are subsets of $\mathbb
R^n_ +$, $\mathbb B$-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-Painlev\'e limit of the convex hull of two points over $\mathbb R^n$
is shown and an explicit extension of $\mathbb B$-convexity is proposed.
