A pseudoline is a simple closed curve in the real projective plane that does not disconnect the projective plane. In other words, the complement of the pseudoline in the projective plane is connected: any two points not on the pseudoline can be joined by a path that does not meet it. Equivalently, a pseudoline is one-sided, with a sufficiently small neighborhood homeomorphic to a Möbius strip instead of an annulus. A pseudoline arrangement is a set of pseudolines in which each pair intersects exactly once (Hernández-Vélez et al. 2017).
Pseudoline
See also
Projective Plane, Pseudolinear Crossing Number, Real Projective PlaneExplore with Wolfram|Alpha
References
Hernández-Vélez, C.; Leaños, J.; and Salazar, G. "On the Pseudolinear Crossing Number." J. Graph Th. 84, 297-310, 2017. https://doi.org/10.1002/jgt.22027.Cite this as:
Weisstein, Eric W. "Pseudoline." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Pseudoline.html