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We present an avatar of the Euler obstruction to foliated structures oncertain non-metric surfaces. This adumbrates (at least for the simplest2D-configurations) that the standard mechanism---to the effect that the devilof algebra sometimes barricades the existence of angelic geometric structures(obstruction theory more-or-less)---propagates slightly beyond the usualmetrical proviso. Alas, the game is much more conservative than revolutionary:in particular we enjoyed retrospecting at Poincar\'e's argument of 1885(announced in 1881).

Euler-Poincar\'e obstruction for pretzels with long tentacles \`a la Cantor-Nyikos