[lilfrost]

I can't believe this is a published article. 3/4 of the paper is essentially crackpottery (e.g. Proposition 5 proves that the composition of surjective maps is surjective), while the final 1/4 is a "proof by picture" (see Figure 6) that you'd see from a mediocre undergraduate pset.

[pavas]

Proposition 5 proves that the composition of surjective maps are _necessarily_ surjective only when the second map is monotone continuous. Based on the definition of surjectivity given, you can have a composition of surjective maps that isn't surjective.

[espeed]

The figures ("pictures") aren't part of the proof, they're part of the presentation, and Figure 6, as stated in the paper, is included as a reference to an analogous work.

[laqq3]

If you read the last 1/4 of the paper, you'll see that Figure 6 is an integral part of the discussion; furthermore, nothing in the discussion is proven rigorously --- they all appeal to the picture.

That is exactly what a proof by picture is.

[nerdponx]

It looks like a manuscript to me.