If you define "a line" as "blocked by another line (standing in for a wall)", it would be non-Euclidean, by virtue of breaking the axiom that says a line can be infinite extended, so that's not a particularly compelling argument.
I don't need to "confuse" geometry and topology. Euclid's axioms require both flat geometry and no "connections" in the space. It's right there in the axioms, if you can read them properly. They have no accommodations for "topology", and it is certainly not just a handwave "oh, whatever, it's no big deal" to extend them to handle it.
I don't need to "confuse" geometry and topology. Euclid's axioms require both flat geometry and no "connections" in the space. It's right there in the axioms, if you can read them properly. They have no accommodations for "topology", and it is certainly not just a handwave "oh, whatever, it's no big deal" to extend them to handle it.