Corrigendum to "Additive colourful Carathéodory type results with an application to radii", Conjecture 4.2:

Sasha Polyanskii has reported us in Budapest during the Discrete Geometry Days II that Conjecture 4.2 is partly incorrect. In fact, if the dimension of the space n is odd, then the constant should be $(n+2)^(1/2)$, and equality would occur if we pick sets of unit vectors {u_i,-u_i}, i=1,...,n+1, such that the first n pairs are vertices of an (n-1)-dimensional regular simplex, and the last pair are orthogonal to the first n pairs of vectors.

Corrigendum to "On large equilateral point-sets in normed spaces", Remark 2.2:

Tomasz Kobos has reported us that Remark 2.2 is incorrect because the function \varphi is not continuous.