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so here is the question

the standard definition of parallel lines are two lines on the same plane that are of an equal distance (hence they will never intersect)

i know there are non-standard or different definitions but i am trying to stay relativly basic here.

i remember reading or hearing somewhere that if space had a positive or negative curvature to it that two parallel lines may actual seperate or intersect. so i have to ask if there is anyone that might be able to explain this, and alsoif they intersect how are they parallel, a part of me thinks that as soon as the distance between them increases or decrease or they intersect, they are not parallel lines so its ok if they intersect.

sorry i know i am getting a bit on a tangent,

i would appreciate any insight, or links so i could learn a bit more, or understand this a bit more.