Individual #non-Euclidean_geometry  geometry based on axioms different from Euclid's
  >part of:  #geometry  the pure mathematics of points and lines and curves and surfaces
  >part:  #hyperbolic_geometry  a non-Euclidean geometry in which it is assumed that through any point there are two or more parallel lines that do not intersect a given line in the plane
  >part:  #elliptic_geometry__Riemannian_geometry  a non-Euclidean geometry that regards space is like a sphere and a line is a great circle

No statement uses or specializes #non-Euclidean_geometry; click here to add one.