A 2-Dimensional Space is a space in which every position can be described using a pair of numbers, such as with a complex number.
Types of 2-Dimensional Space
The spherical plane has a positive curvature, and can be thought of as the two-dimensional space being a sphere, on the surface of a ball. Two parallel lines will eventually wrap around the sphere and meet again, and similarly walking in a straight line will eventually return an entity in a spherical space to its original location.
The Euclidean plane has a zero curvature, and is the ordinary flat plane that follows the postulates of Euclidean geometry.
The hyperbolic plane has a negative curvature. This means that two parallel lines will diverge, giving them the name ultraparallel.