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May 19, 2020 at 17:09 comment added Claus I just wanted to point you to this new post. I think it is great that the grid with the diagonal is getting more and more attention. mathoverflow.net/q/360785/156936
May 19, 2020 at 6:22 comment added Claus this is very impressive! So in fact you have established the equivalence of the crossing-along-diagonals lemma (puzzle theorem) and the topological theorem about separators. I find this quite spectacular and feel this should be made prominent! One would now suspect the crossing-along-diagonals lemma is a simple, powerful tool like the Sperner lemma, but unknown.
May 18, 2020 at 20:55 comment added Wlod AA The central notion which combines the FPP and dimension theory is hardly known at all, it is the notion of universal function -- it is a common generalization of the two theories. It could be applied to differential equations, functional analysis, homotopy theory of manifolds. The general notion of the universal morphisms (and its dual notion) could be applied usefully to several categories, even to algebra (which was already done anyway).
May 18, 2020 at 19:08 history answered Wlod AA CC BY-SA 4.0