As I explained in the first chapter of the booklet "J.C. Maxwell's Void", there are forces in empty regions located far from sources (masses, electric charges) as soon as the laws of electromagnetism apply there.
The demonstration takes place in a geometric and physical context entirely faithful to what the contemporaries of this Scottish physicist could have imagined.
The demonstration technique uses (i) classical vector products, (ii) their projection into the dual space of the vector space E(3, R) referred to a direct orthonormal basis of dimension three, and (iii) the trivial decomposition of these projections.
This protocol can therefore potentially be generalized at several levels: (i) by deforming the vector products, (ii) by projecting the deformed vector products into the dual space in a more sophisticated way, and (iii) by decomposing these projections in non-trivial ways.
These are the topics I will present in the following pages. The topic "Deformed cross products" should actually be seen on vixra.org or in the French language on this website.