[zenorogue]

The phrase "non-euclidean geometry" does not mean "any geometry that violates the Euclid axioms" but specifically that the parallel postulate is replaced. traki is right.

[trakl]

I've got to reconsider given adrusi's comment, I think he's actually right. The parallel postulate is what makes the sum of angles of any triangle to be 180º.

[zenorogue]

Other Euclid's axioms should still hold in non-Euclidean geometry, but with portals and walls, they do not. Mathematicians who are experts in non-Euclidean geometry would agree that portals do not yield non-Euclidean geometry, e.g. Henry Segerman http://twitter.com/henryseg/status/970797060369846273 (see also http://twitter.com/marctenbosch/status/301331439725719552 ).