I added a github issue at https://github.com/metamath/set.mm/issues/3747 
related to parts of this thread.

Benoît

On Tuesday, June 11, 2019 at 1:23:01 AM UTC+2 [email protected] wrote:

> The set of convex combinations of a set of points (i.e. the convex hull of 
> the set of points) is characterized by the followings:
> (1) it is convex and contains the set of points.
> (2) it is contained in any convex set (subset of the underlying space) 
> that contains the set of points.

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