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Topologically Fragmental Space and the Proof of Hadwiger's Conjecture

Cao Zexin
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Abstract

A topological space is introduced in this paper. Just liking the plane, it's continuous, however its $n+1$ regions couldn't be mutually adjacent. Some important phenomenon about its cross-section are discussed. The geometric generating element of the coloring region-map is also an important concept. Every $n$-coloring region map is in the cross-section set of an $n$-color geometric generating element. The proof of four color theorem and Hadwiger's conjecture is obtained by researching them and their cross-sections. And we can see in the context, that those conjectures are not of graph theory, but such topological space.

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Cao Zexin. 2005-04-04. Topologically Fragmental Space and the Proof of Hadwiger's Conjecture. https://arxiv.org/abs/math/0311475

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