An Axiomatic Account of Space as a basis for a Proof of the Four Colour Theorem

Abstract

A definition is given of seriate sets as being sets constituted out of structured collections of objects which are recursively internally self- similar. Fundamental (geometrical) objects of Dimension N are conceived to be constituted out of seriate sets of fundamental objects of Dimension N-1, starting with points assigned to Dimension 0. Syntactical rules to enable such objects to be systematically named and combined, are set out. A series of formal proofs of theorems relative to objects of Dimensions 1 and 2 are worked through. A proof that four colours are sufficient to colour any five area map is given in illustration. I know most/all will think all the above impossible, and necessarily the work of some crazy. If it is wrong I believe it is wrong in interesting ways. The underlying idea is easily grasped without working through the theorems given, so I would be grateful to hear from anyone as to why it is wrong - and not simply because it must be so.